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CRC Press, Taylor & Francis Group, 2014. — XIV, 629 p. — ISBN-13: 978-1-4665-1057-9 (eBook - PDF). With a special emphasis on engineering and science applications, this textbook provides a mathematical introduction to PDEs at the undergraduate level. It takes a new approach to PDEs by presenting computation as an integral part of the study of differential equations. The authors...
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CRC Press, Taylor & Francis Group, 2014. — XIV, 629 p. — ISBN-13: 978-1-4665-1057-9. With a special emphasis on engineering and science applications, this textbook provides a mathematical introduction to PDEs at the undergraduate level. It takes a new approach to PDEs by presenting computation as an integral part of the study of differential equations. The authors use Mathematica...
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Springer, 2012. - 357 pages. ISBN: 3642278922 The term 'control theory' refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is...
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Springer, 2003. — 440 p. This text deals with the singularities of the solutions of several classes of nonlinear partial differential equations and systems. Applications of the results here obtained are given for the Monge-Ampere equation, for quasi-linear systems arising in fluid mechanics, and for some nonlinear integrodifferential equations useful in solid body mechanics in...
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Cambridge University Press, 2010. — 128 p. Its self-contained presentation and 'do-it-yourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation...
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Springer, 2009. — 150 p. This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave...
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Birkhäuser Basel, 2011. — 199 p. — ISBN: 978-0-8176-8114-2 (eBook), 978-0-8176-8113-5 (Hardcover). This self-contained textbook provides the basic, abstracttoolsused innonlinear analysisand their applications to semilinear elliptic boundary value problems.By firstoutlining the advantages and disadvantages of each method, this comprehensive textdisplays how variousapproachescan...
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Cambridge University Press, 2007, 316p. Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the interplay of topological and variational ideas, methods of nonlinear analysis are able to tackle such fundamental problems. This graduate text explains some of the key techniques in a way...
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Springer, 2008. - 204 Pages. This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport...
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Pisa: Scuola Normale Superiore, 2019. - 230 p. - (Publications of the Scuola Normale Superiore) - ISBN 8876426507 This text originated from the Ph.D. course given by the first author at the Scuola Normale Superiore in the academic year 2009-2010. The second and third authors, students of S.N.S. at that time, wrote down the first version of the notes. Since then, the course has been...
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American Mathematical Society, 2018. — 161 p. — (CRM Monograph Series 37). — ISBN 1470442507. In this monograph the authors study the well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable and with boundary data in fractional Hardy–Sobolev and Besov spaces. The...
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Academic Press, 1965. — 511 Pages. In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system...
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New York, Basel: Marcel Dekker, 2003. - 374 p. The papers collected in this volume are concerned with hyperbolic problems, or problems the methods of which are related to hyperbolic techniques. T. NISHITANI introduces a notion of nondegenerate characteristic for systems of linear partial differential equations of general order. He shows that nondegenerate characteristics are...
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Springer, 2004. — 157 Pages. Like all of Vladimir Arnold's books, this book is full of geometric insight. Arnold illustrates every principle with a figure. This book aims to cover the most basic parts of the subject and confines itself largely to the Cauchy and Neumann problems for the classical linear equations of mathematical physics, especially Laplace's equation and the...
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Springer, 2004. — 157 p. — ISBN 3-540-40448-1. Like all of Vladimir Arnold's books, this book is full of geometric insight. Arnold illustrates every principle with a figure. This book aims to cover the most basic parts of the subject and confines itself largely to the Cauchy and Neumann problems for the classical linear equations of mathematical physics, especially Laplace's...
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Academic Press, 2009. — 744 p. — ISBN: 978-0-12-374732-7. Integrating Maple V animation software and traditional topics of partial differential equations, this text discusses first and second-order differential equations, Sturm-Liouville eigenvalue problems, generalized Fourier series, the diffusion or heat equation and the wave equation in one and two spatial dimensions, the...
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Academic Press, 2009. - 744 pages. Integrating Maple V animation software and traditional topics of partial differential equations, this text discusses first and second-order differential equations, Sturm-Liouville eigenvalue problems, generalized Fourier series, the diffusion or heat equation and the wave equation in one and two spatial dimensions, the Laplace equation in two...
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Springer, 2004. — 443 p. — (Operator Theory: Advances and Applications Vol.148) — ISBN 978-3-0348-9622-1. The present monograph is devoted to the construction and investigation of the new high order of accuracy difference schemes of approximating the solutions of regular and singular perturbation boundary value problems for partial differential equations. The construction is...
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University of Missouri. — 440 p. Решебник к книге /file/1276079/ This manual contains solutions with notes and comments to problems from the textbook "Partial Differential Equations with Fourier Series and Boundary Value Problems" (Second Edition). Most solutions are supplied with complete details and can be used to supplement examples from the text. There are also many figures...
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Pearson Education, 2004. — 816 p. — ISBN: 0131480960 Решебник к этой книге: /file/1567779/ This example-rich reference fosters a smooth transition from elementary ordinary differential equations to more advanced concepts. Asmar's relaxed style and emphasis on applications make the material accessible even to readers with limited exposure to topics beyond calculus. Encourages...
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Second Edition. — Pearson Education, Inc, 2005. — 813 p. — ISBN: 0-13-148096-0. Решебник к этой книге: /file/1567779/ For introductory courses in Partial Differential Equations (PDEs) taken by majors in engineering, physics, and mathematics. This example-rich text fosters a smooth transition from elementary ordinary differential equations courses to more advanced concepts in a...
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Springer, 2010. - 199 pages. Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a multitude of applications. Additionally, some of the...
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Cetraro, Italy 2013. — Springer, 2017. — 250 p. Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard...
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Springer International Publishing AG, 2018. — 234 p. — (Progress in Nonlinear Differential Equations and Their Applications: Subseries in Control 90). — ISBN 3319766651. This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic...
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Springer International Publishing AG, 2018. — 240 p. — (Progress in Nonlinear Differential Equations and Their Applications: Subseries in Control 90). — ISBN 3319766651. This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic...
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Springer International Publishing, Switzerland, 2016. — 317 p. — ISBN-10: 3319320602 This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the...
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Birkhauser, 2008. — 205 p. This book examines various mathematical tools—based on generalized collocation methods—to solve nonlinear problems related to partial differential and integro-differential equations. Covered are specific problems and models related to vehicular traffic flow, population dynamics, wave phenomena, heat convection and diffusion, transport phenomena, and...
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Oxford University Press, USA 2006. - 536 pages. Hyperbolic Partial Differential Equations(PDEs), and in particular first-order systems of conservation laws, have been a fashionable topic for over half a century. Many book shave been written, but few of them deal with genuinely multidimensional hyperbolic problems: in this respect the most classical, though not so well-known,...
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Springer, 1969. — 154 p. The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of development and simplicity, and the operator method permits us to exploit thi s theory...
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Wiley, 2010. — 318 pages. The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an...
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Sрringer, 2007. — 283 p. This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of...
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Harvard University, 1972, 83 p. A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing - the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore...
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Routledge, 1961. — 103 p. The book is an introduction both to Laplace's equation and its solutions and to a general method of treating partial differential equations. Chapter 1 discusses vector fields and shows how Laplace's equation arises for steady fields which are irrotational and solenoidal. In the second chapter the method of separation of variables is introduced and used to...
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New York: Chapman & Hall, 2017. — 766 p. Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving...
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New York: Springer, 2010. — 398 p. — ISBN 978-0-387-98612-8 e-ISBN 978-0-387-68028-6. Local Transformations and Conservation Laws Introduction Local Transformations Conservation Laws Noether's Theorem Some Connections Between Symmetries and Conservation Laws Construction of Mappings Relating Differential Equations Introduction Notations; Mappings of...
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Walter de Gruyter GmbH, Berlin/Boston, Germany, 2014. — 205 p. — (De Gruyter Studies in Mathematics 55) — ISBN 978-3-11-031540-0. Elliptic partial differential equations is one of the main and most active areas in mathematics. In our book we study linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent...
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Springer, 2016. — 291 p. — (Universitext). — ISBN 3319489348. This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces,...
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Springer, 2016. — 587 p. — ISBN 3319489348. This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series,...
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Birkhäusеr, Bоston, 2006. — 329 pages. This collection of original articles and surveys treats linear and nonlinear aspects of the theory of partial differential equations. Phase space analysis methods, also known as microlocal analysis, have yielded striking results over the past years and have become one of the main tools of investigation. Equally important is their role in...
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Cambridge: Cambridge University Press, 2016. — 203 p. The area of nonlinear dispersive partial differential equations (PDEs) is a fast developing field which has become exceedingly technical in recent years. with this book, the authors provide a self-contained and accessible introduction for graduate or advanced undergraduate students in mathematics, engineering, and the physical...
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Springer, 2018. — xi+198 p. — (Lecture Notes in Mathematics, 2220). — ISBN 978-3-319-95186-7. The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main underlying ideas, and providing up-to-date...
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Springer, 2012. - 158 pages. The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrödinger and...
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CRC, 2005. - 304 Pages. Separation of Variables for Partial Differential Equations: An Eigenfunction Approach includes many realistic applications beyond the usual model problems. The book concentrates on the method of separation of variables for partial differential equations, which remains an integral part of the training in applied mathematics. The presentation includes,...
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Addison-Wesley Publishing Company, Inc., 1984. — (Encyclopedia of mathematics and its applications; v. 23) Editor’s Statement Foreword by Felix E. Browder Preface Preliminaries Some Inequalities Sequences and Series of Continuous Functions, the Ascoli-Arzela Theorem, and the Weierstrass Approximation Theorem The Lebesgue Dominated-Convergence Theorem, Leibniz’s Rule, and Fubini’s...
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Springer, 1987. — 370 p. The field of nonlinear hyperbolic problems has been expanding very fast over the past few years, and has applications - actual and potential - in aerodynamics, multifluid flows, combustion, detonics amongst other. The difficulties that arise in application are of theoretical as well as numerical nature. In fact, the papers in this volume of proceedings...
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Springer International Publishing, 2016 — 110p. — (SpringerBriefs in Mathematical Physics 12) — ISBN: 978-3-319-33370-0 (eBook), 978-3-319-33369-4 (Softcover). In this volume a theory for models of transport in the presence of a free boundary is developed.Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the...
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Springer, 2001. - 330 pages. The main objective of this monograph is the study of a class of stochastic differential systems having unbounded coefficients, both in finite and in infinite dimension. We focus our attention on the regularity properties of the solutions and hence on the smoothing effect of the corresponding transition semigroups in the space of bounded and...
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Springer International Publishing AG, 2017. — 319 p. — (Applied and Numerical Harmonic Analysis) — ISBN: 9783319527413 This collection of articles and surveys is devoted to Harmonic Analysis, related Partial Differential Equations and Applications and in particular to the fields of research to which Richard L. Wheeden made profound contributions. The papers deal with Weighted Norm...
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North Holland, 1982. — 575 p. Since the fifties, the theory of partial differential equations has undergone considerable development , yet it is certainly one of those fields where we find both the largest number of research articles and the smallest number of works of synthesis. The specialist can come to terms with such a situation, but the student who desires an introduction to...
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World Scientific Publishing, 2010. - 208 pages. ISBN: 9814304832 The book provides a comprehensive overview on the theory on analysis of singularities for partial differential equations. It contains a summarization of the formation, development and main results on this topic. Some of the author's discoveries and original contributions are also included, such as the propagation...
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Springer, 2019. — 455 p. — (Computational Methods in Applied Sciences 47). — ISBN 3319783246. This book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof. William Fitzgibbon, Prof. Yuri Kuznetsov, and Prof. O. Pironneau, whose...
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Springer, 2019. — 455 p. — (Computational Methods in Applied Sciences 47). — ISBN 3319783246. This book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof. William Fitzgibbon, Prof. Yuri Kuznetsov, and Prof. O. Pironneau, whose...
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Elsevier, 2008. — 595 p. — ISBN: 0444532412. This handbook is the sixth and last volume in the series devoted to stationary partial differential equations. The topics covered by this volume include in particular domain perturbations for boundary value problems, singular solutions of semi-linear elliptic problems, positive solutions to elliptic equations on unbounded domains,...
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Elsevier, 2005. — 625 p. — ISBN: 0444520457 A collection of self contained, state-of-the-art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching. Partial differential equations represent one of the most rapidly developing...
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North Holland, 2006. — 630 p. This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with...
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Univеrsity Of Chicаgo Prеss, 2001. — 360 p. Alberto P. Calderón (1920-1998) was one of this century's leading mathematical analysts. His contributions, characterized by great originality and depth, have changed the way researchers approach and think about everything from harmonic analysis to partial differential equations and from signal processing to tomography. In addition,...
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Birkhäuser Basel, 2009. - 352 pages. This volume includes several invited lectures given at the International Workshop "Analysis, Partial Differential Equations and Applications", held at the Mathematical Department of Sapienza University of Rome, on the occasion of the 70th birthday of Vladimir G. Maz'ya, a renowned mathematician and one of the main experts in the field of...
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Springer, 2014. — 431 p. This book collects papers mainly presented at the "International Conference on Partial Differential Equations: Theory, Control and Approximation" (May 28 to June 1, 2012 in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions. The contributors are leading experts from all over the world, including members of the...
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Springer, 2019. — 505 p. — (Series in Contemporary Mathematics 03). — ISBN 981133031X. This is the first book on the subject of the periodic unfolding method (originally called "éclatement périodique" in French), which was originally developed to clarify and simplify many questions arising in the homogenization of PDE's. It has since led to the solution of some open problems....
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Singapore: World Scientific, 2017. — 301 p. The book extensively introduces classical and variational partial differential equations (PDEs) to graduate and post-graduate students in Mathematics. The topics, even the most delicate, are presented in a detailed way. The book consists of two parts which focus on second order linear PDEs. Part I gives an overview of classical PDEs,...
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Elsevier Science, 2002. — 665 p. This volume is the 14 th and last one of the series "Nonlinear Partial Differential Equations and their Applications. Coll~ge de France Seminar", which published the texts of the lectures given at the seminars organized by Jacques-Louis Lions, from his election at the Coll~ge de France in 1973 until his retirement in 1998. It was one of the...
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Second Edition. — CRC Press, 2013. — 654 p. An Introduction to Partial Differential Equations with MATLAB, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the...
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Springer International Publishing AG, 2017. — 398 p. — (Trends in Mathematics) — ISBN 978-3-319-62361-0. Daniel Alpay graduated in 1986 from the Weizmann Institute of Science with the Ph.D. thesis: “Reproducing kernel Krein spaces of analytic functions and inverse scattering” under the supervision of Prof. Harry Dym. After graduating, he occupied positions at the University of Tel...
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Pitman Advanced Publishing Program, 1980. — 239 p. Maximum principles Entire solutions of elliptic equations Analytic solutions of partial differential equations Analytic continuation Runge's theorem Pseudoanalytic functions The backwards heat equation The inverse scattering problem
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New York, USA: Dover Publication, Inc., 1988. — 320 p. — ISBN 0394358279, 0486438341. Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include...
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Pitman Publishing, 1976. — 148 p. Elliptic Equations in Two Independent Variables Analytic Continuation Integral Operators Complete Families of Solutions The Bergman Kernel Function Inverse Methods in Compressible Fluid Flow Parabolic Equations in One Space Variable Integral Operators Reflection Principles Initial-Boundary Value Problems Parabolic Equations in Two Space Variables...
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Springer Science+Business Media, 1998. — 541 Pages. ISBN: 1461272661 The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. Introduction to Partial Differential Equations with MATLAB is a careful integration of traditional core topics with modern topics, taking full advantage of the computational power of...
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Cambridge University Press, 1975. — 292 p. In this book, Professor Copson gives a rigorous account of the theory of partial differential equations of the first order and of linear partial differential equations of the second order, using the methods of classical analysis. In spite of the advent of computers and the applications of the methods of functional analysis to the...
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Wiley, 2016. — 574 p. — ISBN-10: 1119189470. — ISBN-13: 978-1119189473 Features new results and up-to-date advances in modeling and solving differential equations Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications presents the needed tools and topics to study the various classes of functional...
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New York: Dover Publications, 2012. — 661 p. I have designed this book as a course for senior year or first-year graduate students in mathematics and mathematically-oriented beginning graduate students in engineering and the applied sciences. Its aim is to fill the gap between elementary textbooks that deal almost exclusively with separation of variables and integral transform...
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New York: Dover Publications, 2012. — 661 p. Contents: Title Page Copyright Page Preface Acknowledgements Introduction The Wave Equation The Heat Equation Laplace's Equation Potential Theory and Fredholm Integral Equations Scattering Theory References Index
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Global Media, 2009. - 124 pages Introduction to Partial Differential Equations This book is intended as a Partial Differential Equations reference for individuals who already posses a firm understanding of ordinary differential equations and at least have a basic idea of what a partial derivative is. This book is meant to be easily readable to engineers and scientists while still...
  • №72
  • 12,30 МБ
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Springer Science+Business Media, 1999. — 277 p. — ISBN: 0817641211 Nonlinear partial differential equations has become one of the main tools of mod­ ern mathematical analysis; in spite of seemingly contradictory terminology, the subject of nonlinear differential equations finds its origins in the theory of linear differential equations, and a large part of functional analysis...
  • №73
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North Holland, 2008. — 608 р. The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts. Review of new results in the area.
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Goteborg: Chalmers University of Technology and University of Geteborg, 1996. — 144 p. Introduction. Dirichlet Problem for Lipschitz Domain. The Setup. Proofs of Theorem 1.1 and Theorem 1.2. Proof of Theorem 1.6. Proof of Theorem 1.3. Proof of Theorem 1.4. Dirichlet Problem for Lipschitz domains. The final arguments for the L2-theory. Existence of solutions to Dirichlet...
  • №75
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N.-Y.: Springer, 2009. — 230 p. In May 2006, The University of Utah hosted an NSF-funded minicourse on stochastic partial differential equations. The goal of this minicourse was to introduce graduate students and recent Ph.D.s to various modern topics in stochastic PDEs, and to bring together several experts whose research is centered on the interface between Gaussian analysis,...
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W. H. Freeman, 2012. — 335 p. — ISBN 1429275928, 9781429275927. Drawing on his decade of experience teaching the differential equations course, John Davis offers a refreshing and effective new approach to partial differential equations that is equal parts computational proficiency, visualization, and physical interpretation of the problem at hand.
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New York: W.H.Freeman, 2012. — 335 p. Drawing on his decade of experience teaching the differential equations course, John Davis offers a refreshing and effective new approach to partial differential equations that is equal parts computational proficiency, visualization, and physical interpretation of the problem at hand.
  • №78
  • 2,86 МБ
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Birkhauser, 1997. - 593 pages. This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma...
  • №79
  • 3,95 МБ
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Birkhäuser Boston, 2011. - 883 pages. The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications. In an effort to make the book more useful for a diverse readership, updated modern examples of applications are chosen from areas...
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American Mathematical Society, 2015. — 92 p. — (Memoirs of the American Mathematical Society v.234, №1103) — ISBN 1470409836. The Hamiltonian defined on functions on $\mathbb{R}\times X$, where $X$ is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. The author considers perturbations of this Hamiltonian, given by polynomial...
  • №81
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Springer, 2012. - 483 Pages. The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions. This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for...
  • №82
  • 4,39 МБ
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CRC, 2003. — 511 p. — ISBN: 0824740394 Offering in-depth analyses of current theories and approaches related to Sobolev-type equations and systems, this reference is the first to introduce a classification of equations and systems not solvable with respect to the highest order derivative, and it studies boundary value problems for these classes of equations. Presenting 2200...
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  • 6,16 МБ
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Springer Basel AG, 2011. - 355 pages. Operator Theory: Advances and Applications. Vol. 211 This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original...
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  • 3,47 МБ
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McGraw Hill, 1968. — 382 p. — ISBN 9780070163966, 0070163960. Partial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables. While focusing on the three most classical partial differential equations (PDEs)—the wave, heat, and Laplace equations—this...
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Springer, 1987. — 174 p. Let me begin by explaining the meaning of the title of this book. In essence, the book studies boundary value problems for linear partial differ­ ential equations in a finite domain in n-dimensional Euclidean space. The problem that is investigated is the question of the dependence of the nature of the solvability of a given equation on the way in which...
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  • 5,49 МБ
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Springer, 2018. — 199 p. — ISBN 978-3-030-00448-4. This book, which is a continuation of Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, presents recent trends and developments upon fractional, first, and second order semilinear difference and differential equations, including degenerate ones. Various stability, uniqueness, and existence results are...
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  • 1,76 МБ
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Sрringer, 1993. - 402 pages. Mathematicians have only recently begun to understand the local structure of solutions of degenerate and singular parabolic partial differential equations. The problem originated in the mid '60s with the work of DeGiorgi, Moser, Ladyzenskajia and Uraltzeva. This book will be an account of the developments in this field over the past five years. It...
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  • 14,33 МБ
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Birkhäuser, 2010. — 403 p. — ISBN 978-0-8176-4551-9. This text is meant to be a self-contained, elementary introduction to Partial Differential Equations, assuming only advanced differential calculus and some basic LP theory. Although the basic equations treated in this book, given its scope, are linear, we have made an attempt to approach them from a nonlinear perspective....
  • №89
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2nd ed. — De Gruyter, 2014. — 291 p. — (de Gruyter Textbook). — ISBN: 311031665X, 9783110316650, e-ISBN: 9783110316674 This book presents a first introduction to PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles...
  • №90
  • 3,49 МБ
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Walter de Gruyter, 2007. - 245 pages. This textbook presents a first introduction to PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types of PDEs, and to acquire some classical...
  • №91
  • 8,12 МБ
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Wiley, 2018. — 382 p. — ISBN 1119221781. Covers multivariable calculus, starting from the basics and leading up to the three theorems of Green, Gauss, and Stokes, but always with an eye on practical applications. Written for a wide spectrum of undergraduate students by an experienced author, this book provides a very practical approach to advanced calculus starting from the basics...
  • №92
  • 6,03 МБ
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Oxford University Press, 2010. — 368 p. Most nonlinear differential equations arising in natural sciences admit chaotic behavior and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as...
  • №93
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New York: Chapman and Hall/CRC, 2011. - 335p. Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces). Stable Solutions of Elliptic Partial Differential Equations offers a...
  • №94
  • 3,74 МБ
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Cham: Springer, 2018. — 273 p. This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as...
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  • 3,24 МБ
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Springer, 1995. - 208 Pages. The book contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and...
  • №96
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Springer, 1998. — 265 p. From the reviews of the first printing, published as volume 30 of the Encyclopaedia of Mathematical Sciences: "... I think the volume is a great success and an excellent preparation for future volumes in the series. ... the introductory style of Egorov and Shubin is .. attractive. ... a welcome addition to the literature and I am looking forward to the...
  • №97
  • 8,36 МБ
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Birkhauser, 2004. — 394 p. The theory of parabolic equations, a well-developed part of the contemporary partial differential equations and mathematical physics, is the subject theory of of an immense research activity. A continuing interest in parabolic equations is caused both by the depth and complexity of mathematical problems emerging here, and by its importance in specific...
  • №98
  • 13,45 МБ
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Walter de Gruyter, 2009. - 290 pages. This text contains a series of self-contained reviews on the state of the art in different areas of partial differential equations, presented by French mathematicians. Topics include qualitative properties of reaction-diffusion equations, multiscale methods coupling atomistic and continuum mechanics, adaptive semi-Lagrangian schemes for the...
  • №99
  • 1,94 МБ
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New York: Springer, 2017. — 257 p. This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed...
  • №100
  • 3,35 МБ
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Springer International Publishing AG, 2017. — 261 p. — (Mathematical Engineering) — ISBN: 3319552112. This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in...
  • №101
  • 5,18 МБ
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American Mathematical Society, 2011. — 410 p. his book is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form. The first three chapters are on elementary distribution theory and Sobolev spaces with many examples and applications to...
  • №102
  • 6,77 МБ
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Providence: American Mathematical Society, 2015. — 210 p. This volume contains the proceedings of the Conference on Spectral Theory and Partial Differential Equations, held from June 17–21, 2013, at the University of California, Los Angeles, California, in honor of James Ralston's 70th Birthday. Papers in this volume cover important topics in spectral theory and partial...
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  • 1,50 МБ
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Springer, 1999. — 316 p. — Series: Springer Undergraduate Mathematics Series. — ISBN-10: 3540761241 ISBN-13: 978-3540761242 This is the practical introduction to the analytical approach taken in Volume 2 . Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables...
  • №104
  • 3,41 МБ
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UC Berkeley, Department of Mathematics. — 213 p. Introduction . Overview. Themes. Entropy and equilibrium . Thermal systems in equilibrium. Examples. Simple fluids. Other examples. Physical interpretations of the model. Equilibrium. Positivity of temperature. Extensive and intensive parameters. Concavity of S. Convexity of E. Entropy maximization, energy...
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Lecture Notes. — The George Washington University Press, 2010. — 101 p. These lecture notes are intended to supplement a one-semester graduate-level engineering course at The George Washington University in numerical methods for the solution of partial differential equations. Both finite difference and finite element methods are included. The main prerequisite is a standard...
  • №106
  • 1,11 МБ
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American Mathematical Society, 2017. — 330 p. — (Mathematical Surveys and Monographs 224). — ISBN 1470437856. Partial dynamical systems, originally developed as a tool to study algebras of operators in Hilbert spaces, has recently become an important branch of algebra. Its most powerful results allow for understanding structural properties of algebras, both in the purely algebraic...
  • №107
  • 2,37 МБ
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Dover, 1993. - 414 pages. This highly useful text for students and professionals working in the applied sciences shows how to formulate and solve partial differential equations. Realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems and numerical and approximate methods. Suggestions for further reading. Solution guide...
  • №108
  • 13,06 МБ
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European Mathematical Society, 2017. — 212 p. — (Zurich Lectures in Advanced Mathematics) — ISBN: 3037191708 The Monge-Ampère equation is one of the most important partial differential equations, appearing in many problems in analysis and geometry. This monograph is a comprehensive introduction to the existence and regularity theory of the Monge-Ampère equation and some selected...
  • №109
  • 2,09 МБ
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Arkansas Tech University, 2013. — 258 p. Contents. The Basics of the Theory of Partial Di_erential Equation. Review of Some ODE Results. First Order Partial Di_erential Equations. Second Order Linear Partial Di_erential Equations. The Laplace Transform Solutions for PDEs. The Fourier Transform Solutions for PDEs. Answers and Solutions. Index.
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Wadsworth Publishing Company, 1982. - 484 pages. The same, refined Ordinary Differential Equations with Modern Applications by Finizio and Lades is the backbone of this text. In addition to this are included applications, techniques and theory of partial difference equations, difference equations and Fourier analysis. This book is designed for an introductory, one-semester...
  • №111
  • 5,64 МБ
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Princeton University Press, 1995. - 352 Pages. ISBN: 0691043612 Second Edition The second edition of Introduction to Partial Differential Equations, which originally appeared in the Princeton series Mathematical Notes, serves as a text for mathematics students at the intermediate graduate level. The goal is to acquaint readers with the fundamental classical results of partial...
  • №112
  • 14,31 МБ
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Cambridge: At the University Press, 1906. — 478 pages. Introduction: two existence theorems. Cauchy's theorem. Linear equations and complete linear systems. Non-linear equations. Equations of the first order. The method of characteristics for two independent variables. Singular integrals. The method of characteristics in any number of independent variables. Lie's...
  • №113
  • 33,89 МБ
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Cambridge: At the University Press, 1906. — 478 p. Introduction: two existence theorems. Cauchy's theorem. Linear equations and complete linear systems. Non-linear equations. Equations of the first order. The method of characteristics for two independent variables. Singular integrals. The method of characteristics in any number of independent variables. Lie's method....
  • №114
  • 4,00 МБ
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Cambridge University Press, 1906. — 596 p. This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our...
  • №115
  • 6,75 МБ
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London: Dover Publications, 2005. — 368 p. This self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to solving a variety of problems in partial differential equations. A major portion of the text is based on material included in the books of L. Schwartz, who developed the theory of...
  • №116
  • 17,85 МБ
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North-Holland, 1983. — 477 p. Nonlinear equations come to us in tremendous variety, each with its own questions and its own difficulties. At one extreme are the completely integrable equations, with constants of the motion and a rich algebraic structure. At the other extreme is chaos, with turbulent solutions and statistical averages. Between these two possibilities, algebraic and...
  • №117
  • 2,72 МБ
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Chapman and Hall/CRC, 2004. — 376 p. Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Pólya in the 1930's and rediscovered in part several times since, it was...
  • №118
  • 2,21 МБ
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Chapman and Hall/CRC, 2006. - 528 p. Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics,...
  • №119
  • 3,35 МБ
  • дата добавления неизвестна
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Birkhauser, 2004. — 377 p. — (Progress in Nonlinear Differential Equations and Their Applications Volume 56) — ISBN-13: 978-1-4612-7396-7. This book introduces a new, state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations; much of the text is dedicated to the application of this method to a wide class of...
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  • 41,58 МБ
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Boca Raton, USA: CRC Press, Taylor & Francis Group, 2018 (First published 1995). — 336 p. — (Studies in Advanced Mathematics). — ISBN 13 978-1-315-89303-7. Fourier Analysis and Partial Differential Equations presents the proceedings of the conference held at Miraflores de la Sierra in June 1992. These conferences are held periodically to assess new developments and results in the...
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  • 87,61 МБ
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Springer, 2014. — 258 p. — ISBN: 3319105442 This volume of papers presented at the conference in honor of Calixto P. Calderón by his friends, colleagues, and students is intended to make the mathematical community aware of his important scholarly and research contributions in contemporary Harmonic Analysis and Mathematical Models applied to Biology and Medicine, and to...
  • №122
  • 1,87 МБ
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N.-Y: Springer, 2015. — 218 p. This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents...
  • №123
  • 1,38 МБ
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Cambridge: Cambridge University Press, 2016. - 364p. In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities. Here, the authors take the unique approach of investigating differential inequalities rather than equations, the reason being that the simplest way to study an equation is...
  • №124
  • 1,81 МБ
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Cambridge University Press, 2016. — 364 p. — ISBN-10: 1107138388. — ISBN-13: 978-1107138384 In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities. Here, the authors take the unique approach of investigating differential inequalities rather than equations, the reason being that the...
  • №125
  • 1,77 МБ
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Birkhäuser, 2010. — 294 p. — (Progress in Nonlinear Differential Equations and Their Applications 79). — ISBN: 978-0-8176-4651-6, 978-0-8176-4173-3. The main focus of this textbook, in two parts, is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. The...
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  • 1,85 МБ
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Basel: Birkhäuser, 2001. — 262 p. The purpose of this publication is to present, in one book, various approaches to analytic problems that arise in the context of singular spaces. It is based on the workshop 'Approaches to Singular Analysis' which was held on April 8-10, 1999, at Humboldt University of Berlin. The aim of this workshop was to bring together young mathematicians...
  • №127
  • 8,80 МБ
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Sрringer, 1984. - 530 pages. This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It is suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost...
  • №128
  • 4,02 МБ
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Academic Press, 1969. - 306 Pages. ISBN: 0122830504 Volume 54 in Mathematics in Science and Engineering In traditional treatments of the partial differential equations of mathematical physics, particular stress is laid on solving boundary value problems and initial-boundary value problems. The reasons are that these problems were the natural ones to consider in classical...
  • №129
  • 4,94 МБ
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Kluwer, 1992. — 278 p. This volume develops the method of Newton's polyhedron for solving some problems in the theory of partial differential equations. The content is divided into two parts. Chapters 1-4 consider Newton's polygon and Chapters 5-7 consider Newton's polyhedron. The case of the polygon makes it possible not only to consider general constructions in the...
  • №130
  • 3,27 МБ
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Springer Science + Business Media B.V., 2008. - 294 pages. For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications...
  • №131
  • 3,11 МБ
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Philadelphia: SIAM, 2002. - 614 pages. The book equally emphasizes classical and modern techniques of solution of partial differential equations. First of all it will be useful for acquaintance of students with new approaches based on the application of such software packages as Mathematica, Matlab or Maple.
  • №132
  • 12,65 МБ
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Philadelphia: SIAM, 2011. — 666 p. Partial differential equations (PDEs) are essential for modeling many physical phenomena. This undergraduate textbook introduces students to the topic with a unique approach that emphasizes the modern finite element method alongside the classical method of Fourier analysis. Additional features of this new edition include broader coverage of PDE...
  • №133
  • 7,36 МБ
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Springer, 2014. — 321 p. Particle Systems and PDEs, Braga, Portugal, December 2012. This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations I, which took place at the Centre of Mathematics of the University of Minho, Braga, Portugal, from the 5th to the 7th of December, 2012. The purpose of the conference was to bring...
  • №134
  • 3,51 МБ
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Springer, 2015. — 395 p. Particle Systems and PDEs II, Braga, Portugal, December 2013. This book focuses on mathematical problems concerning different applications in physics, engineering, chemistry and biology. It covers topics ranging from interacting particle systems to partial differential equations (PDEs), statistical mechanics and dynamical systems. The purpose of the second...
  • №135
  • 6,88 МБ
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Springer, 2016. — 352 p. Particle Systems and PDEs III, Braga, Portugal, December 2014. The main focus of this book is on different topics in probability theory, partial differential equations and kinetic theory, presenting some of the latest developments in these fields. It addresses mathematical problems concerning applications in physics, engineering, chemistry and biology that...
  • №136
  • 3,48 МБ
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Springer, 2017. — 309 p. PSPDE IV, Braga, Portugal, December 2015. "This book addresses mathematical problems motivated by various applications in physics, engineering, chemistry and biology. It gathers the lecture notes from the mini-course presented by Jean-Christophe Mourrat on the construction of the various stochastic “basic” terms involved in the formulation of the dynamic...
  • №137
  • 5,31 МБ
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N.-Y.: Springer, 2015. - 368p. This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of...
  • №138
  • 6,95 МБ
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World Scientific, 2000. — 224 p. The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler–Lagrangian equations....
  • №139
  • 5,79 МБ
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Department of Mathematics, University of California, Santa Barbara, 2010. - 96 pages. These lecture notes arose from the course "Partial Di erential Equations" - Math 124A taught by the author in the Department of Mathematics at UCSB in the fall quarters of 2009 and 2010. The selection of topics and the order in which they are introduced is based on Walter A. Strauss. Partial...
  • №140
  • 2,10 МБ
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Birkhäuser Boston, 1986. - 511 Pages. Pseudo differential methods are central to the study of partial differential equations, because they permit an 'algebraization', a replacement of compositions of operators in n-space by simpler product rules for their symbols. The main purpose of this book is to set up an operational calculus for operators defined from differential and...
  • №141
  • 4,81 МБ
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Singapore: World Scientific Publishing Co, 2015. — 348 p. This book aims to introduce some new trends and results on the study of the fractional differential equations, and to provide a good understanding of this field to beginners who are interested in this field, which is the authors' beautiful hope. This book describes theoretical and numerical aspects of the fractional...
  • №142
  • 2,44 МБ
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Editors: Matthew J. Gursky, Ermanno Lanconelli, Andrea Malchiodi, Gabriella Tarantello, Xu-Jia Wang, Paul C. Yang, Sun-Yung Alice Chang, Antonio Ambrosetti. — Springer, 2009. — 273 p. — (Lecture Notes in Mathematics 1977). — ISBN 978-3-642-01673-8; 978-3-642-01674-5. This volume contains lecture notes on some topics in geometric analysis, a growing mathematical subject which...
  • №143
  • 1,52 МБ
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Dover, 1997. - 476 pages. ISBN: 0486612716 Excellent undergraduate/graduate-level introduction presents full introduction to the subject and to the Fourier series as related to applied mathematics, considers principal method of solving partial differential equations, examines 1st-order systems, computation methods, and much more. Over 600 problems and exercises, with answers...
  • №144
  • 3,58 МБ
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2nd Edition. — Springer International Publishing, 2016. — 225 p. — (Progress in Nonlinear Differential Equations and Their Applications. Volume 89) — ISBN: 9783319433721 Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory...
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  • 2,12 МБ
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N.-Y.: Springer, 2015 - 449p. This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of...
  • №146
  • 8,76 МБ
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5th edition. — Pearson Education, 2012. — 784 p. — ISBN-10: 0321797051 This book emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations. Coverage includes Fourier series, orthogonal functions, boundary value problems, Green’s functions, and transform methods. This text is ideal for readers...
  • №147
  • 13,73 МБ
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China Machine Press, 2003. — 769 p. Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations. Topics addressed include heat equation, method of separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, finite difference numerical methods for partial...
  • №148
  • 14,33 МБ
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Prentice Hall, 1987. — 532 p. This text discusses elementary partial differential equations in the engineering and physical sciences. It is suited for courses whose titles include Fourier series, orthogonal functions, or boundary value problems. It may also be used in courses on Green's functions or transform methods. Simple models (heat flow, vibrating strings and membranes)...
  • №149
  • 3,88 МБ
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4th edition. — Prentice Hall, 87 p. In this manual there are solutions to most of the starred exercises of "Applied Partial Differential Equations: with Fourier Series and Boundary Value Problems", by Richard Haberman. Over 1000 exercises of varying difficulty form an essential part of this text. It is hoped that these approximately 250 selected solutions will toe useful for...
  • №150
  • 5,60 МБ
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4th edition. — Prentice Hall, 87 p. In this manual there are solutions to most of the starred exercises of "Applied Partial Differential Equations: with Fourier Series and Boundary Value Problems", by Richard Haberman. Over 1000 exercises of varying difficulty form an essential part of this text. It is hoped that these approximately 250 selected solutions will toe useful for...
  • №151
  • 6,96 МБ
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2nd Edition. — Springer, 2017. — 465 p. — (Springer Series in Computational Mathematics 18). — ISBN 978-3-662-54960-5. This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite...
  • №152
  • 3,17 МБ
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Springer-Verlag, Berlin, 2003, 311 pages. The book offers a simultaneous presentation of the theory and of the numerical treatment of elliptic problems. The author starts with a discussion of the Laplace equation in the classical formulation and its discretisation by finite differences and deals with topics of gradually increasing complexity in the following chapters. He...
  • №153
  • 9,71 МБ
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European Mathematical Society, 2007. — 305 p. — (EMS Textbooks in Mathematics) — ISBN: 3037190426 It is the main aim of this book to develop at an accessible, moderate level an L*2* theory for elliptic differential operators of second order on bounded smooth domains in Euclidean n-space, including a priori estimates for boundary-value problems in terms of (fractional) Sobolev...
  • №154
  • 1,81 МБ
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Mineola: Dover Publications, 2006. - 412 p. A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, this treatment advances to the theory of weighted...
  • №155
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Cambridge University Press, 2005. — 216 p. — (London Mathematical Society Lecture Note Series 318) — ISBN: 0521574919 Perturbation of the boundary is a rather neglected topic in the study of PDEs for two main reasons. First, on the surface it appears trivial, merely a change of variables and an application of the chain rule. Second, carrying out such a change of variables...
  • №156
  • 1,26 МБ
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Springer, 1981. — 352 p. — (Lecture Notes in Mathematics 840). — ISBN 978-3-540-10557-2, 978-3-540-38528-8. Introduction Preliminaries Examples of nonlinear parabolic equations in physical, biological and engineering problems Existence, uniqueness and continuous dependence Dynamical systems and liapunov stability Neighborhood of an equilibrium point Invariant manifolds near an...
  • №157
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Cambridge: CUP, 2007.- 285p. Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of...
  • №158
  • 1,33 МБ
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Berlin: Springer, 2011. - 530p. The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader...
  • №159
  • 9,16 МБ
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Springer International Publishing AG, Switzerland, 2016. – 139 p. – ISBN-10: 3319224697 The first book to introduce certified reduced basis methods for parametrized partial differentiation equations Unique focus on both the mathematical aspects and algorithmic elements of the methods Essential examples provide a point of departure for the development of more advanced...
  • №160
  • 3,25 МБ
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Springer, 2016. — 139 p. During the past decade, reduced order modeling has attracted growing interest in computational science and engineering. It now plays an important role in delivering high-performance computing (and bridging applications) across industrial domains, from mechanical to electronic engineering, and in the basic and applied sciences, including neurosciences,...
  • №161
  • 3,26 МБ
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Springer, 1988. — 434 p. This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.
  • №162
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N.-Y.: Wiley, 2012. - 696p. Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential...
  • №163
  • 85,32 МБ
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N.-Y.: Springer, 2010. - 311p. The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs. In this, the second edition, the authors build on the theory of SPDEs driven by space-time Brownian motion, or more generally, space-time Lévy process noise. Applications of the theory are...
  • №164
  • 3,60 МБ
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Springer-Verlag Berlin Heidelberg 2011. — (Applied Mathematical Sciences 152). — 362 pp. — ISBN: 978-3-642-23910-6 (Print) 978-3-642-23911-3 (Online). Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical...
  • №165
  • 7,35 МБ
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Springer-Verlag, 1983. — 392 p. — Series: Grundlehren Der Mathematischen Wissenschaften. ISBN-10: 0387121390 ISBN-13: 978-0387121390. The present Vol. II is mainly devoted to operators with constant coefficients. An analysis of the existence and regularity of (fundamental) solutions in the first two chapters is followed by a thorough study of the Cauchy problem. One chapter is...
  • №166
  • 10,32 МБ
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Springer, 2007. — 537 p. Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades...It is a superb book, which must be present in every mathematical library, and an...
  • №167
  • 5,00 МБ
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Springer, 1985. — 359 p. Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades...It is a superb book, which must be present in every mathematical library, and an...
  • №168
  • 2,81 МБ
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Springer, 1990. — 452 p. The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen­ tial equations. In particular, it could also serve as an introduction...
  • №169
  • 2,75 МБ
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Springer, 1997. — 301 p. — (Mathématiques et Applications). — ISBN 10 3540629211, ISBN 13 978-3540629214. In this introductory textbook, a revised and extended version of well-known lectures by L. H?rmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the...
  • №170
  • 5,36 МБ
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Springer, 2011. — 145 p. There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general...
  • №171
  • 1002,09 КБ
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Chapman and Hall/CRC, 2005. — 417 p. The field of control theory in PDEs has broadened considerably as more realistic models have been introduced and investigated. This book presents a broad range of recent developments, new discoveries, and mathematical tools in the field. The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between...
  • №172
  • 3,17 МБ
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3rd Edition. — Springer International Publishing AG, 2017. — 414 p. — (Applied Mathematical Sciences 127) — ISBN: 3319516574 This book describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. The topic is of substantial and growing interest for many scientists and engineers and accordingly to graduate students...
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Springer, 2006. — 358 p. The topic of the inverse problems is of substantial and rapidly growing interest for many scientists and engineers. The second edition covers most important recent developments in the field of inverse problems, describing theoretical and computational methods, and emphasizing new ideas and techniques. It also reflects new changes since the first edition,...
  • №174
  • 1,91 МБ
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Royal Institute of Technology, 1999. — 81 p. This is the first web edition of a course taught 1997-1999 at the Royal Institute of Technology (KTH, Stockholm) to graduate students in physics, engineering and quantitative social sciences. Realizing the need of an introductory text giving a comparative overview of a variety of methods commonly used to solve partial differential...
  • №175
  • 2,60 МБ
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Academic Press, 2002. - 394 Pages. This book is written to meet the needs of undergraduates in applied mathematics, physics and engineering studying partial differential equations. Many books deal with partial differential equations, some at an elementary level and others at more advanced levels, so it is necessary that some justification should be given for the publication...
  • №176
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N.-Y.: SIAM, 2011. — 235 p. This book presents a systematic theory of Taylor expansions of evolutionary-type stochastic partial differential equations (SPDEs). The authors show how Taylor expansions can be used to derive higher order numerical methods for SPDEs, with a focus on pathwise and strong convergence. In the case of multiplicative noise, the driving noise process is...
  • №177
  • 1,39 МБ
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Springer, 1991. - 249 pages. Identifies significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. This book contains a chapter on Lewy's example of a linear equation without solutions.
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  • 3,12 МБ
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Springer International Publishing, Switzerland, 2016. — 515 p. — (Developments in Mathematics 36) — ISBN 3319290231. This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is...
  • №179
  • 6,42 МБ
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R.S. Johnson & Ventus Publishing ApS, 2012. — 156 p. — ISBN 9788776819699. Most descriptions of physical systems, as used in physics, engineering and, above all, in applied mathematics, are in terms of partial differential equations. This text, presented in three parts, introduces all the main mathematical ideas that are needed for the construction of solutions. The material...
  • №180
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Second Edition. — Springer, 2007. — 356 p. This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical...
  • №181
  • 13,77 МБ
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Third Edition. — Springer, 2013. — 415 p. — ISBN 978-1-4614-4808-2. This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these...
  • №182
  • 2,72 МБ
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Springer International Publishing AG, Switzerland, 2016. – 146 p. – ISBN-10: 3319342185 This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time...
  • №183
  • 1,88 МБ
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New York: Springer, 2015. - 123p. The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard...
  • №184
  • 3,61 МБ
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Springer International Publishing AG, 2018. — 310 p. — (Mathematics for Industry 31) — ISBN 3319679422. This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It...
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  • 4,35 МБ
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New York: Prentice Hall, 2002. — 530 p. This extremely readable book illustrates how mathematics applies directly to different fields of study. Focuses on problems that require physical to mathematical translations, by showing readers how equations have actual meaning in the real world. Covers fourier integrals, and transform methods, classical PDE problems, the Sturm-Liouville...
  • №186
  • 5,60 МБ
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Wadsworth & Brooks/Cole Advanced Books & Software, 1990. — 547 p. — ISBN: 0534122167 This is a text for a two-semester or three-quarter sequence of courses in partial differential equations. It is assumed that the student has a good background in vector calculus and ordinary differential equations and has been introduced to such elementary aspects of partial differential...
  • №187
  • 11,05 МБ
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N.-Y.: Springer, 2000. - 637p. This volume contains a broad treatment of important partial differential equations, particularly emphasizing the analytical techniques. In each chapter the author raises various questions concerning the particular equations discussed therein, discusses different methods for tackling these equations, gives applications and examples, and concludes...
  • №188
  • 16,70 МБ
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Springer, 2017. — 235 p. This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time. Based on the author’s extensive research in the area of controllability theory, this monograph specifically focuses on the issues of controllability,...
  • №189
  • 2,78 МБ
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Cambridge University Press, 2018. — 255 p. — (Encyclopedia of Mathematics and its Applications). — ISBN 978-1-107-18882-2. Starting from physical motivations and leading to practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It shows the ways in which these equations link different fields...
  • №190
  • 3,12 МБ
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Springer International Publishing Switzerland, 2015 — 337 pp. — (Applied Mathematical Sciences 190). — ISBN: 978-3-319-11085-1 (Print) 978-3-319-11086-8 (Online). This book gives a concise introduction to the basic techniques needed for the theoretical analysis of the Maxwell Equations, and filters in an elegant way the essential parts, e.g., concerning the various function...
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Department of Mathematics, Princeton University, 72 pages. Content Basic definitions and examples General Equations General Ideas Main Equations Regularity or Break-down Main Goals Great Open Problems in PDE References
  • №192
  • 523,71 КБ
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Springer Science+Business Media, LLC 2009. — 161 pages. ISBN: 1441910956 This concise book covers the classical tools of PDE theory used in today's science and engineering: characteristics, the wave propagation, the Fourier method, distributions, Sobolev spaces, fundamental solutions, and Green's functions. The approach is problem-oriented, giving the reader an opportunity to...
  • №193
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Springer, 1995. — 277 p. The smoothness of solutions for quasilinear systems is one of the most important problems in modern mathematical physics. This book deals with regular or strong solutions for general quasilinear second-order elliptic and parabolic systems. Applications in solid mechanics, hydrodynamics, elasticity and plasticity are described. The results presented are...
  • №194
  • 1,36 МБ
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John Wiley & Sons Inc, 1988. - 410 pages. This book is devoted to the development of complex function theoretic methods in partial differential equations and to the study of analytic behaviour of solutions. It presents basic facts of the subject and includes recent results, emphasizing the method of integral operators and the method of differential operators. The first chapter...
  • №195
  • 6,58 МБ
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Boca Raton: CRC Press, 1992. — 307 p. Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and Complex Analysis explores the background and plumbs the depths of this symbiosis.The book is...
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  • 2,41 МБ
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Basel: Birkhäuser, 1993. - 355p. This monograph provides the first survey of Floquet theory for partial differential equations with periodic coefficients. The author investigates, among others, hypoelliptic, parabolic, elliptic and Schrödinger equations, and boundary value problems arising in applications. In particular, results are given about completeness of the set of...
  • №197
  • 6,42 МБ
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2003. - 151 pages. Review Of Advanced Calculus. Continuous Functions Of One Variable. Exercises. Theorems About Continuous Functions. The Integral. Upper And Lower Sums. Exercises. Functions Of Riemann Integrable Functions. Properties Of The Integral. Fundamental Theorem Of Calculus. Exercises. Multivariable Calculus. Continuous Functions. Sufficient Conditions For...
  • №198
  • 775,01 КБ
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Birkhauser Basel, 1997. - 264 pages. Semilinear elliptic equations play an important role in many of mathematics and its applications to physics and other sciences. This book presents a wealth of modern methods to solve such equations, including the systematic use of the Pohozaev identities for the description of sharp estimates for radial solutions and the fibring method....
  • №199
  • 4,54 МБ
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CRC Press, 1997. — 378 p. — ISBN: 0849378532 This book provides an accessible treatment of this demanding subject. The authors integrate the use of Mathematica throughout the book rather than just providing a few sample problems at the end of chapters. Although rich in the theory for developing underlying mathematical analysis, the text emphasizes the development of methods....
  • №200
  • 11,97 МБ
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2 edititon. — Chapman and Hall/CRC, 2002. — 440 p. This book provides an accessible treatment of this demanding subject. The authors integrate the use of Mathematica throughout the book rather than just providing a few sample problems at the end of chapters. Although rich in the theory for developing underlying mathematical analysis, the text emphasizes the development of...
  • №201
  • 1,29 МБ
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2nd Edition. — Springer-Verlag, Berlin, Heidelberg, 2003. — 882 p. — (Texts in Computational Science and Engineering 1) — ISBN: 9783642628115 During the last decades there has been a tremendous advancement of computer hardware, numerical algorithms, and scientific software. Engineers and scientists are now equipped with tools that make it possible to explore real world...
  • №202
  • 93,91 МБ
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AMS, 2006. — 230 pages. — ISBN: 0821835769 The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a...
  • №203
  • 3,32 МБ
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American Mathematical Society, 2006. — 230 p. The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. The first seven chapters of this book, based on notes of lectures delivered at Stanford in...
  • №204
  • 3,71 МБ
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Springer, 2018. — 259 p. — (Universitext). — ISBN 3319783890. This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic...
  • №205
  • 3,61 МБ
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Springer, 2018. — 230 p. — (Universitext). — ISBN 3319783890. This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic...
  • №206
  • 8,60 МБ
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Basel: Birkhauser, 2016. - 395p. Covers the whole spectrum of partial differential equations, from modeling, analysis, to numerical analysis with numerical illustrations Covers the major deterministic numerical methods used in scientific computing practice Mathematically self-contained This book is devoted to the study of partial differential equation problems both from the...
  • №207
  • 8,86 МБ
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World Scientific, 2009. — 544 Pages. This book presents the theory of diffusion-reaction equations starting from the Volterra-Lotka systems developed in the eighties for Dirichlet boundary conditions. It uses the analysis of applicable systems of partial differential equations as a starting point for studying upper-lower solutions, bifurcation, degree theory and other nonlinear...
  • №208
  • 3,83 МБ
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World Scientific Publishing Co Pte Ltd, 2014 - 193 p. In this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest. It gives a selfcontained introduction to research in the last decade concerning global problems in the theory of submanifolds, leading to some types of Monge-Amp#65533;re equations.From the methodical point of...
  • №209
  • 2,45 МБ
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Hoboken: Wiley, 1994. - 330p. A systematic presentation of the global classical solution and the global classical discontinuous solution to quasilinear hyperbolic systems. This book is a result of the author's research on the Cauchy problem, boundary value problems, free boundary problems and the generalised Riemann problem.
  • №210
  • 2,79 МБ
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World Scientific Publishing, 2010. - 464 pages. ISBN-10: 9814322881 This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without...
  • №211
  • 6,77 МБ
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World Scientific, 1996 (2005 reprint). - 439 pages. This book is an introduction to the general theory of second order parabolic differential equations, which model many important, time-dependent physical systems. It studies the existence, uniqueness, and regularity of solutions to a variety of problems with Dirichlet boundary conditions and general linear and nonlinear...
  • №212
  • 3,89 МБ
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Academic Press, 1972. — 299 p. This book is written in four modular parts intended as easy steps for the student. The intention here is to lead him from an elementary level to a level of modern analysis research. Thus the first pages of Part I are an explanation of the regular (classical) solutions of the second-order wave equation in two-space-time, while the latter pages of Part...
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World Scientific, 2014. — 176 p. — ISBN: 9814616389 This volume is on initial-boundary value problems for parabolic partial differential equations of second order. It rewrites the problems as abstract Cauchy problems or evolution equations, and then solves them by the technique of elementary difference equations. Because of this, the volume assumes less background and...
  • №214
  • 1,24 МБ
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New York: Springer, 2016. - 73 p. Provides concise though comprehensive overview on the topic This book will appeal to a wide readership, from graduate students to researchers Enriches understanding on the topic This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures...
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  • 1,22 МБ
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N.-Y.: Springer, 2015. - 266p. This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such...
  • №216
  • 2,07 МБ
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N.-Y.: Wiley. 2008. - 398p. Praise for the First Edition: "This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds." —SIAM Review A practical introduction to nonlinear PDEs and their real–world applications Now in a Second Edition, this...
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  • 15,43 МБ
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2nd ed. — Wiley, 2008. — 415 p. — ISBN: 9780470225950 A practical introduction to nonlinear PDEs and their real-world applications Now in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and...
  • №218
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N.-Y.: Springer, 2015. - 304p. This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". The audience consists of students in mathematics, engineering, and the sciences. The topics include derivations of some of the standard models of mathematical physics and...
  • №219
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Springer, 2004. - 224 pages. From the reviews of the second edition: "This second edition of the short undergraduate text provides a fist course in PDE aimed at students in mathematics, engineering and the sciences. The material is standard … . Strong emphasis is put on modeling and applications throughout; the main text is supplied with many examples and exercises." (R....
  • №220
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2nd Edition. — Springer, 2004. — 221 p. — (Undergraduate Texts in Mathematics). — ISBN 0387209352. This text is written for the standard, one-semester, undergraduate course in elementary partial differential equations. The topics include derivations of some of the standard equations of mathematical physics (including the heat equation, the wave equation, and Laplace's equation)...
  • №221
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Springer International Publishing AG, 2017. — 517 p. — (Universitext) — ISBN 3319586459. Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and...
  • №222
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Springer, 2017. — 261 p. — (Mathematical Engineering). — ISBN 978-3-319-55211-8. This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics....
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Springer, 2019. — 383 p. — ISBN 3319906461. This book was written based on lectures and tutorials held for mathematics and computer science students. Supplementary notions were added to these notes in order to make the reader refer to the bibliography as little as possible. The present form of the book is due to the essential contributions of our published results. We divided the...
  • №224
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Springer, 2006. — 206 pages. This book presents selected topics in science and engineering from an applied-mathematics point of view. The described natural, socioeconomic, and engineering phenomena are modeled by partial differential equations that relate state variables such as mass, velocity, and energy to their spatial and temporal variations. Typically, these equations are...
  • №225
  • 16,13 МБ
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Society for Industrial & Applied Mathematics, 2005. — 665 p. Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects...
  • №226
  • 6,17 МБ
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Paris: European Mathematical Society, 2018. — 443 p. The present book is a detailed exposition of the author and his collaborators’ work on boundedness, continuity, and differentiability properties of solutions to elliptic equations in general domains, that is, in domains that are not a priori restricted by assumptions such as “piecewise smoothness” or being a “Lipschitz graph”....
  • №227
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Lecture Notes. - Department of Mathematics, Leipzig University, 2012. - 205 pages. Introduction Examples Equations from variational problems Exercises Equations of first order Linear equations Quasilinear equations Nonlinear equations in two variables Nonlinear equations in Rn Hamilton-Jacobi theory Exercises Classification Linear equations of second order...
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Translated from the Russian by P.C. Sinha, Cand. Sc. — Moscow: Mir publishers, 1978. — 408 p. Contents: Introduction. Classification of equations. Formulation of some problems. The Lebesgue integral and some questions of functional analysis. Function spaces. Elliptic equations. Hyperbolic equations. Parabolic equations.
  • №229
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New York: Addison-Wesley Publishing Co., 1977. - 291p. This book is concerned with the relationship between the symmetries of a linear partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions via separation of variables, and the properties of the special functions that arise in this manner. It is shown how the...
  • №230
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N.-Y.: Springer, 2013. - 460p. The theory of distributions constitutes an essential tool in the study of partial differential equations. This textbook would offer, in a concise, largely self-contained form, a rapid introduction to the theory of distributions and its applications to partial differential equations, including computing fundamental solutions for the most basic...
  • №231
  • 4,14 МБ
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2nd Edition. — Springer, 2018. — 615 p. — (Universitext). — ISBN 978-3-030-03295-1. The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. The book is written in a format suitable for a graduate course spanning...
  • №232
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Kendall/Hunt Publishing Company, 2003. — 164 p. Contents. Power Series. Symmetry and Orthogonality. Fourier Series. Partial Differential Equations. PDE’s in Higher Dimensions. Using Mathematica to solve differential equations. Index.
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Birkhauser, 2006. - 778 pages. One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applications in every branch of applied mathematics, physics, and engineering, including fluid dynamics, elasticity, and optics....
  • №234
  • 4,92 МБ
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Second Edition. — Elsevier North Holland Inc., 1982. — 396 p. — ISBN 0-444-00352-5. Introduction. Mathematical Models. Classification of Second-order Equations. The Cauchy Problem. Fourier Series. Method of Separation of Variables. Eigenvalue problems. Boundary Value Problems. Higher Dimensional Problems. Green's Function. Integral Transforms. Appendix.
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Elsevier Publishing Company, 1973. — 383 p. — ISBN 0-444-00132-8. Introduction. Mathematical Models. Classification of Second-order Equations. The Cauchy Problem. Fourier Series. Method of Separation of Variables. Eigenvalue problems. Boundary Value Problems. Higher Dimensional Problems. Green's Function. Integral Transforms. Appendix.
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New York: Springer, 2012. - 388 p. Nečas’ book Direct Methods in the Theory of Elliptic Equations, published 1967 in French, has become a standard reference for the mathematical theory of linear elliptic equations and systems. This English edition presents Nečas’ work essentially in the form it was published in 1967. It gives a timeless and in some sense definitive treatment of...
  • №237
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Lecture Notes. — Monterey, California: Department of Mathematics Naval Postgraduate School, 2002. — 355 p. Contents. Introduction and Applications . Basic Concepts and Definitions. Applications. Conduction of Heat in a Rod. Boundary Conditions. A Vibrating String. Boundary Conditions. Diffusion in Three Dimensions. Classification and Characteristics . Physical...
  • №238
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Harlow: Longman Higher Education, 1992. - 332p. This book addresses the theory and applications of mathematical models that involve (a) nonlinear operations; (b) differentiation; and (c) the presence of singular objects (like measures or non-differentiable functions). Classical nonlinear analysis can certainly deal with (a) and (b) , while the theory of distributions has...
  • №239
  • 9,72 МБ
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Oxford University Press, 2003. — 464 p. — ISBN 0 19 852770 5. Partial differential equations are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. This new edition of Applied Pdes contains many new sections and exercises Including, American options, transform methods, free surface flows, linear elasticity and complex...
  • №240
  • 8,27 МБ
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(Oxford Texts in Applied and Engineering Mathematics) Publisher: Oxford University Press, USA, 2003. - 464 Pages. Partial differential equations are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. This new edition of Applied PDEs contains many new sections and exercises Including, American options, transform...
  • №241
  • 10,19 МБ
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Publisher: Springer; 2014 edition (November 9, 2013), Series: Undergraduate Texts in Mathematics, Hardcover: 635 pages, ISBN-10: 9400778198 ISBN-13: 978-9400778191 This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science,...
  • №242
  • 8,36 МБ
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Cambridge University Press, 1995. — 525 p. — ISBN 0-521-47811-1. Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and...
  • №243
  • 4,72 МБ
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Wiley, 2014. — 452 p. — 3rd ed. — ISBN: 1118629949, 9781118629949 A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and...
  • №244
  • 36,21 МБ
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John Wiley & Sons, 2008. — 496 pages. 2 edition ISBN: 0470133902 A rigorous, yet accessible, introduction to partial differential equations — updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics,...
  • №245
  • 6,50 МБ
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Wiley, 2014. — 130 p. — 3rd ed. — (Pure and Applied Mathematics). — ISBN: 1118630092, 9781118630099 As the Solutions Manual, this book is meant to accompany the main title, Beginning of Partial Differential Equations, Third Edition. The Third Edition features a challenging, yet accessible, introduction to partial differential equations, and provides a solid introduction to partial...
  • №246
  • 1,17 МБ
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N.-Y.: Springer, 2015. - 412p. This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations. Many illustrative examples also show techniques for finding such solutions in terms of integrals. Particular attention is given to developing the fundamentals of...
  • №247
  • 2,29 МБ
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Springer, 2015. — 412 p. — ISBN: 3319201395, 9783319201399 This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations. Many illustrative examples also show techniques for finding such solutions in terms of integrals. Particular attention is given to...
  • №248
  • 3,42 МБ
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Springer, 2012. — 223 p. — ISBN: 3642244149 Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings. And yet even the linear theory of these equations is...
  • №249
  • 3,47 МБ
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1997. - 415p. The book Partial Differential Equations through Examples and Exercises has evolved from the lectures and exercises that the authors have given for more than fifteen years, mostly for mathematics, computer science, physics and chemistry students. By our best knowledge, the book is a first attempt to present the rather complex subject of partial differential...
  • №250
  • 15,30 МБ
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American Mathematical Society, 1982. — 169 p. — (Proceedings of Symposia in Pure Mathematics, vol. 4). A collection of essays addressed at the meeting of proceedings of the fourth symposium in pure mathematics of the American Mathematical Society held at the University of California, Berkeley, California, April 21-22, 1960. Extensions and Applications of the De Giorgi-Nash...
  • №251
  • 3,65 МБ
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Springer International Publishing AG, 2017. — 469 p. — (Association for Women in Mathematics Series 5) — ISBN 3319515918. This book is the second of a two volume series. Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book features fully-refereed, high-quality papers exploring new results and trends in weighted norm...
  • №252
  • 8,07 МБ
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Springer International Publishing, Switzerland, 2016. — 380 p. — (Association for Women in Mathematics Series. Volume 4). — ISBN: 9783319309590. Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book contains survey and expository articles by leading experts in their corresponding fields, and features fully-refereed,...
  • №253
  • 7,42 МБ
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Dover Publications Inc. , 1992. - 245 pages. Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text.
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  • 1,80 МБ
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Amsterdam: De Gruyter, 2011. - 489p. This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space setting is a highly adaptable and suitable...
  • №255
  • 2,76 МБ
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Cambridge University Press, 2005. — 384 p. A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, paying particular emphasis to developing an appreciation of underlying mathematical theory. Beginning with basic definitions,...
  • №256
  • 1,91 МБ
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Springer Netherlands 1979. — (Mathematical Physics Studies 1). — 140 pp. — ISBN: 978-90-277-1036-9 (Print) 978-94-009-9511-6 (Online). The aim of this paper is to show that the theory of jet bundles supplies the appropriate setting for the study of Backlund trans­ formations. These transformations are used to solve certain partial differential equations, particularly non-linear...
  • №257
  • 4,32 МБ
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Cambridge University Press, 2010. - 630 pages. Do you want a rigorous book that remembers where PDEs come from and what they look like? This highly visual introduction to linear PDEs and initial/boundary value problems connects the math to physical reality, all the time providing a rigorous mathematical foundation for all solution methods. Readers are gradually introduced to...
  • №258
  • 5,87 МБ
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New York: CRC, 2001. — 515 p. This book contains about 3000 first-order partial differential equations with solutions. New exact solutions to linear and nonlinear equations are included. The text pays special attention to equations of the general form, showing their dependence upon arbitrary functions. At the beginning of each section, basic solution methods for the corresponding...
  • №259
  • 7,30 МБ
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Second Edition. — New York: Chapman and Hall/CRC, 2016. — 1623 p. Includes nearly 4,000 linear partial differential equations (PDEs) with solutions Presents solutions of numerous problems relevant to heat and mass transfer, wave theory, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction theory, quantum mechanics, chemical engineering sciences,...
  • №260
  • 29,20 МБ
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Second Edition. — CRC Press, 2012. — 1912 pages. New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear...
  • №261
  • 34,60 МБ
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Academic Press, 2005. - 520 Pages. Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at...
  • №262
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Boca Raton: CRC Press, 2016. - 292p. The ordinary Laplacian is defined as the ordinary second derivative of a function of one variable or the sum of the ordinary second partial derivatives of a function of a higher number of variables in a physical or abstract Caresian space. Physically, the ordinary Laplacian describes an ordinary diffusion process in an isotropic medium...
  • №263
  • 9,38 МБ
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World Scientific, 2004. — 193 p. — ISBN: 9812387641 This book presents, for the first time, a systematic formulation of the geometric theory of noncommutative PDE's which is suitable enough to be used for a mathematical description of quantum dynamics and quantum field theory. A geometric theory of supersymmetric quantum PDE's is also considered, in order to describe quantum...
  • №264
  • 26,84 МБ
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New York: Marcel Dekker. - 2002. - 477 p. In recent years the theory of stochastic partial differential equations has had an intensive development and many important contributions have been obtained. The first results on stochastic evolution equations started to appear in the early 1960s and were motivated by physics, filtering, and control theory. SPDEs are also deeply connected...
  • №265
  • 3,47 МБ
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Boston: de Gruyter, 2013. — 295 p. The text is intended for students who wish a concise and rapid introduction to some main topics in PDEs, necessary for understanding current research, especially in nonlinear PDEs. Organized on three parts, the book guides the reader from fundamental classical results, to some aspects of the modern theory and furthermore, to some techniques of...
  • №266
  • 1,29 МБ
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Cambridge University Press, 2011. — 744 p. The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working...
  • №267
  • 4,21 МБ
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Birkhauser, 2008. — 472 p. The monograph is focused on presentation of recent results on some nonlinear parabolic-hyperbolic systems of partial differential equations arising from physics, mechanics and material science. Most of the results presented in this book are based on the original research of the author starting in 1997. The book is self-contained and the material is well...
  • №268
  • 18,01 МБ
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Springer, 2015. — 296 p. — (UNITEXT 92) — ISBN: 9783319154305, 9783319154312 This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a...
  • №269
  • 2,36 МБ
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Springer, 1998. — 456 p. Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 23-28, 1997. This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of...
  • №270
  • 3,20 МБ
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Cairo, Egypt: Hindawi Publishing Corporation, 2008. — 205 p. — (Contemporary Mathematics and Its Applications 06). — ISBN 9774540395. The book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they...
  • №271
  • 2,12 МБ
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CRC Press, 2015. — 320 p. — ISBN: 9781498703413, EIBSN: 9781498703444 Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The...
  • №272
  • 2,50 МБ
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World Scientific Pub, 1990. - 152 pages. This series of lecture notes includes various parts of the theory of mixed type partial differential equations with boundary conditions such as: the classical dynamical equation of mixed type due to S. A. Chaplygin (1904), regularity of solutions in the sense of the first pioneer in the field F. G. Tricomi (1923) and in brief his...
  • №273
  • 1,58 МБ
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Springer, 2004. — 447 p. Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis, and...
  • №274
  • 4,26 МБ
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Springer, 2004. — 447 p. — ISBN 978-0-387-00444-0. Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory,...
  • №275
  • 3,37 МБ
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Walter de Gruyter, 2008. - 316 pages. ISBN-10: 3110191539 This book deals with the reliable verification of the accuracy of approximate solutions which is one of the central problems in modern applied analysis. After giving an overview of the methods developed for models based on partial differential equations, the author derives computable a posteriori error estimates by...
  • №276
  • 3,73 МБ
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Birkhäusеr Bаsel, 2005, 282 pages Vsevolod Alekseevich Solonnikov is known as one of the outstanding mathematicians from the St. Petersburg Mathematical School. His remarkable results on exact estimates of solutions to boundary and initial-boundary value problems for linear elliptic, parabolic, Stokes and Navier-Stokes systems, his methods and contributions to the...
  • №277
  • 2,65 МБ
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Kluwer Academic Publisher, 1996. — 432 p. — (Mathematics and its applications, v. 384). — ISBN 0-7923-4303-4. This volume endeavours to summarise all available data on the theorems on isomorphisms and their ever increasing number of possible applications. It deals with the theory of solvability in generalised functions of general boundary-value problems for elliptic equations. In...
  • №278
  • 3,59 МБ
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Springer-Verlag, 1978. — 154 p. — (Lecture Notes in Mathematics) ISBN: 3540089519 The nonlinear method in the theory of distributions presented in this work is based on embeddings of the distributions in D' 0{ n) into associative and commutative algebras whose elements are classes of sequences of smooth functions on R n. The embeddings define various distribution...
  • №279
  • 4,13 МБ
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Elsevier Science Ltd, 1987. — 428 pages. — Series: North-Holland Mathematical Library ISBN-10: 0444703101 ISBN-13: 978-0444703101 During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed...
  • №280
  • 2,53 МБ
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Springer Basel, 2013. — 457 pages. ISBN-10: 3034805128 This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo-) monotone or accretive operators as fast as possible towards the analysis of concrete differential...
  • №281
  • 4,65 МБ
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2nd Edition. — Springer International Publishing, Switzerland, 2015. — 710 p. — ISBN 978-3-319-15092-5. This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations (PDEs) during the last few years at...
  • №282
  • 6,65 МБ
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3rd Edition. — Springer International Publishing, Switzerland, 2016. — 699 p. — (UNITEXT – La Matematica per il 3+2. 99) — ISBN: 9783319312378 This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations...
  • №283
  • 8,53 МБ
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Springer, 2008. - 450 pages. This book is designed as an advanced undergraduate or a first-year graduatecourse for students from various disciplines like applied mathematics,physics, engineering. The main purpose is on the one hand to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences; on the other hand to...
  • №284
  • 5,76 МБ
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Springer-Verlag Italia, 2013. — 480 pages. ISBN: 8847028612 This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations during the last decade at the Politecnico of Milan. The main purpose of these...
  • №285
  • 6,81 МБ
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Springer, 2015. — 433 p. — ISBN 978-3-319-15415-2. This book is designed for advanced undergraduate students from various disciplines, including applied mathematics, physics, and engineering. It evolved during the PDE courses that both authors have taught during recent decades at the Politecnico di Milano, and consists of problems of various types and difficulties. In the first...
  • №286
  • 3,96 МБ
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Cambridge University Press, 2001. - 385 pages. This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. It brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are...
  • №287
  • 10,84 МБ
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London: London School of Economics, 2017. — 142 p. Introduction. First Order PDEs. The classical trinity. Separation of variables. Integral transform methods. Distributions and weak solutions. Bibliography. Index.
  • №288
  • 8,31 МБ
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Springer, 2012. - 462 pages. This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this first volume, special emphasis is placed on geometric and complex variable methods involving integral representations. The following topics are treated: integration...
  • №289
  • 3,61 МБ
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Springer, 2006. — 456 p. — ISBN-10 3-540-34457-8. This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables.In this first volume, special emphasis is placed on geometric and complex variable methods involving integral representations. The following topics are treated:...
  • №290
  • 3,88 МБ
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Springer, 2006. — 400 p. — ISBN-10 3-540-34461-6. This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this second volume, special emphasis is placed on functional analytic methods and applications to differential geometry. The following topics are treated:...
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  • 3,69 МБ
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Springer, 2012. - 469 pages. This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this second volume, special emphasis is placed on functional analytic methods and applications to differential geometry. The following topics are treated: solvability of...
  • №292
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World Scientific Publishing, 2017. — 262 p. — ISBN 9789813226692. This book is directed toward the numerical integration (solution) of a system of partial differential equations (PDEs) that describes a combination of chemical reaction and diffusion, that is, reaction-diffusion PDEs. The particular form of the PDEs corresponds to a system discussed by Alan Turing and is therefore...
  • №293
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Berlin; Heidelberg; New York: Springer-Verlag, 2003. — 196 p. — (Lecture Notes in Computational Science and Engineering 29 ) — ISBN-13:978-3-540-00351- 9 e-ISBN-13: 978-3-642-59325-3. This item can be delivered to the solution or its gradient. These new discretization techniques are promising approaches to overcome the severe problem of mesh-generation. Furthermore, the easy...
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Springer, 2000. - 538 pages. This two-volume work mainly addresses undergraduate and graduate students in the engineering sciences and applied mathematics. Hence it focuses on partial differential equations with a strong emphasis on illustrating important applications in mechanics. The presentation considers the general derivation of partial differential equations and the...
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Providence: American Mathematical Society, 2013. — 354 p. On May 11, 2012, Professor Patrizia Pucci turned 60. In celebration of Patrizia Pucci’s birthday, a conference was held at the University of Perugia during May 28 and June 1, 2012. The main purpose of this scientific meeting has been to bring together leading experts and researchers in nonlinear partial differential...
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Wiley. 2018. — 213 p. — ISBN 978-1-119-50796-3. Solve engineering and scientific partial differential equation applications using the PDE2D software developed by the author This book derives and solves a range of ordinary and partial differential equation (PDE) applications. This book describes an easy-to-use, general purpose, and time-tested PDE solver developed by the author...
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Providence: American Mathematical Society, 2001. — 174 p. This research monograph establishes many new results in the area of singular quasilinear elliptic and parabolic partial differential equations and is mainly motivated by three of the author's previous papers, [Shi], [LfS], and [LgS]. The singularities that arise are described by weights which often can be associated with...
  • №298
  • 1,21 МБ
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Princeton University Press, 2015. — 288 p. — ISBN: 0691161291. This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis...
  • №299
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Berlin: Springer, 2011. — 487 p. Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods....
  • №300
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Springer, 2018. — 295 p. — (Operator Theory: Advances and Applications 26). — ISBN 3319912135. This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses the...
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Austin, Texas, 1977. — 219 p. OCR . Elements of Hilbert Space . Linear Algebra. Convergence and Continuity. Completeness. Hilbert Space. Dual Operators; Identifications. Uniform Boundedness; Weak Compactness. Expansion in Eigenfunctions. Distributions and Sobolev Spaces . Distributions. Sobolev Spaces. Trace. Sobolev's Lemma and Imbedding. Density and Compactness....
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Springer, 1972. — 242 p. In this paper we were especially concerned with two aims: First, to make the presentation rather self-contained and not to use too many references to other papers (except, in using well-known theorems). Secondly, we especially cared to supply detailed proofs, even at those points where this implies cumbersome labour and one is tempted to "leave the proof...
  • №303
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D. Van Nostrand Company , 1967. — 226 p. Too frequently, undergraduates taking courses for an honours degree in mathelnatics first encounter partial differential equations in the mathematical physics part of their curricula, when solutions to the elementary problems that occur are conjured ad hoc from nowhere, as if by magic. Thus I have found undergraduates quite surprised to...
  • №304
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Princeton University Press, 2010 - 344 p. This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems. Andrey Smyshlyaev and Miroslav Krstic develop explicit...
  • №305
  • 7,94 МБ
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Dover Publications, 2006. — 352 p. — ISBN: 0486452972, 9780486452975 Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory. Topics include ordinary differential equations in more than two variables,...
  • №306
  • 23,29 МБ
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Prentice Hall, 1999. - 658 pages. Offering a welcome balance between rigor and ease of comprehension, this book presents full coverage of the analytic (and accurate) method for solving PDEs - in a manner that is both decipherable to engineers and physically insightful for mathematicians. By exploring the eigenfunction expansion method based on physical principles instead of...
  • №307
  • 7,15 МБ
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Prentice Hall, 1999. — 667 p. — ISBN 0-13-674359-5. Offering a welcome balance between rigor and ease of comprehension, this book presents full coverage of the analytic (and accurate) method for solving PDEs - in a manner that is both decipherable to engineers and physically insightful for mathematicians. By exploring the eigenfunction expansion method based on physical principles...
  • №308
  • 3,51 МБ
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Walter de Gruyter, 2003. - 162 pages. Modeling, in particular with partial differential equations, plays an ever growing role in the applied sciences. Hence its mathematical understanding is an important issue for today's research. This book provides an introduction to three different topics in partial differential equations arising from applications. The subject of the...
  • №309
  • 1,10 МБ
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World Scientific Publishing Company, 2004. - 320 pages. Second Edition This textbook is a self-contained introduction to Partial Differential Equations (PDEs). It is designed for Undergraduate and first year graduate students who are mathematics, physics, engineering or, in general, science majors. The goal is to give an introduction to the basic equations of mathematical...
  • №310
  • 11,73 МБ
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World Scientific, 2004. - 320 pages. Second Edition OCR-слой This textbook is a self-contained introduction to Partial Differential Equations (PDEs). It is designed for Undergraduate and first year graduate students who are mathematics, physics, engineering or, in general, science majors. The goal is to give an introduction to the basic equations of mathematical physics and...
  • №311
  • 1,51 МБ
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Cambridge University Press, 2000. — 590 p. — Series: Encyclopedia of Mathematics and its Applications (Book 80) OCR ISBN-10: 0521880157 ISBN-13: 978-0521780889. Here is a lucid and comprehensive introduction to the differential geometric study of partial differential equations (PDE). The first book to present substantial results on local solvability of general and nonlinear...
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2nd edition. — John Wiley & Sons, 2007. — 464 p. — ISBN: 0470054565 Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing...
  • №313
  • 2,74 МБ
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Wiley, 1992. - 440 Pages. Covers the fundamental properties of partial differential equations (PDEs) and proven techniques useful in analyzing them. Uses a broad approach to illustrate the rich diversity of phenomena such as vibrations of solids, fluid flow, molecular structure, photon and electron interactions, radiation of electromagnetic waves encompassed by this subject as...
  • №314
  • 5,43 МБ
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Hoboken: Wiley, 2007. — 691 p. Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a...
  • №315
  • 31,79 МБ
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Cambridge University Press, 2008. — 233 p. This book deals with equations that have played a central role in the interplay between partial differential equations and probability theory. Most of this material has been treated elsewhere, but it is rarely presented in a manner that makes it readily accessible to people whose background is probability theory. Many results are given...
  • №316
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Springer, 2007, 302p., 4th edition. Contents: The Direct Methods in the Calculus of Variations Lower Semi-continuity Constraints Compensated Compactness The Concentration-Compactness Principle Ekeland’s Variational Principle Duality Minimization Problems Depending on Parameters Minimax Methods The Finite Dimensional Case The Palais-Smale Condition A General...
  • №317
  • 2,53 МБ
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Springer, 1999. — 563 pages. This text provides an introduction to the theory of partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and...
  • №318
  • 5,69 МБ
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Springer, 2010. - 678 pages. The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment...
  • №319
  • 4,50 МБ
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Springer, 2010. — 614 Pages. This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts,...
  • №320
  • 3,27 МБ
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Springer, 2010. — 715 p. The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic...
  • №321
  • 3,72 МБ
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Research World, 2012. - 116 pages. ISBN: 9788132334446, 8132334442. Table of Contents. Chapter 1 - Maxwell's Equations. Chapter 2 - Navier–Stokes Existence and Smoothness. Chapter 3 - Noether's Theorem. Chapter 4 - Method of Characteristics and Method of Lines. Chapter 5 - Ricci Flow. Chapter 6 - Secondary Calculus and Cohomological Physics, Screened Poisson Equation and...
  • №322
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World Scientific, 1994. - 350 pages. ISBN: 9810213514 This text is devoted to boundary value problems for general partial differential equations. It develops efficient methods of resolution of boundary value problems for elliptic equations, based on the theory of analytic functions, having great theoretical and practical importance. A new approach to the investigation of...
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Gordon and Breach, 1970 (1966). — 132 pages. — (Notes on Mathematics and Its Applications) ISBN: 0677025203 ISBN-13: 9780677025209 Covers existence and approximation theorems in functional analysis, L-squared inequalities, necessary and sufficient conditions for existence of solutions (variable coefficients), and L-squared estimates and pseudo-convexity. Includes further...
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  • 4,25 МБ
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Applied Mathematics University of Washington, 2005. — 195 pages. This short book is intended for a one-semester course for students in the sciences and engineering after they have taken one year of calculus and one term of ordinary differential equations. For universities on quarter systems, sections labelled "optional" can be omitted without loss of continuity. A course based...
  • №325
  • 786,04 КБ
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Springer, 1998. - 392 Pages. This book teaches the basic methods of partial differential equations and introduces related important ideas associated with the analysis of numerical methods for those partial differential equations. Standard topics such as separation of variables, Fourier analysis, maximum principles, and energy estimates are included. Numerical methods are...
  • №326
  • 1,95 МБ
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Springer-Verlag, 2011. — 128 pages. — ISBN: 085729783X The subject of Partial Differential Equations (PDEs) which first emerged in the 18th century holds an exciting and special position in the applications relating to the mathematical modelling of physical phenomena. The subject of PDEs has been developed by major names in applied mathematics such as Euler, Legendre,...
  • №327
  • 3,09 МБ
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Springer, 2018. — 175 p. — (Pseudo-Differential Operators: Theory and Applications 13). — ISBN 331992706X. Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic. The operators which make up the main subject of the book can be characterized in...
  • №328
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3rd. ed. — Bookboon.com, 2018. — 172 p. The contents of this book came into existence during the time the author has been teaching a course on partial differential equations and on operator theory for about twenty years. Let us discuss the contents somewhat more closely. Basically, the book contains topics from distribution theory, from operator theory, and from operator...
  • №329
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3rd ed. — bookboon.com, 2018. — 248 p. Operators in Hilbert space. Operator semigroups and Markov processes. Holomorphic semigroups. Elements of functional analysis. Bibliography. Index.
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Springer Basel AG 2011. — 658 p. — (Monographs in Mathematics 101). — ISBN 978-3-0346-0536-6. The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics....
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Springer, Basel, 2014. — 796 p. — (Monographs in Mathematics. Volume 104) — ISBN: 3034808127 If we had to formulate in one sentence what this book is about, it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The...
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Singapore: World Scientific, 2011. — 295 p. Fourier multiplier, function space X s p,q Navier-Stokes equation Strichartz estimates for linear dispersive equations Local and global wellposedness for nonlinear dispersive equations The low regularity theory for the nonlinear dispersive equations Frequency-uniform decomposition techniques Conservations, Morawetz' estimates of...
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N.-Y.: Springer, 2015. - 79p. This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how...
  • №334
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Springer, 2009. — 700 p. — ISBN: 3642002501 "Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts....
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  • 13,67 МБ
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Department of Mathematics Saint Xavier University. — Beijing: Higher Education Press; Springer 2009. — 746 p. Nonlinear Physical Science focuses on recent advances of fundamental theories and principles,analytical and symbolic approaches, as well as computational techniques in nonlinear physical science and nonlinear mathematics with engineering applications.
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New York: Dover Publications, 1995. — 480 p. It has become customary at many colleges and universities to teach undergraduate courses in boundary value problems, Fourier series, and integral transforms. These courses usually emphasize the Fourier series or Laplace transforms, and then treat some problems in partial differential equations as applications. In teaching such a...
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  • 4,11 МБ
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Dover Publications, 1995. — 456 p. — ISBN 0-486-68648-X. It has become customary at many colleges and universities to teach undergraduate courses in boundary value problems, Fourier series, and integral transforms. These courses usually emphasize the Fourier series or Laplace transforms, and then treat some problems in partial differential equations as applications. In teaching...
  • №338
  • 13,43 МБ
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Springer, 1996. — 440 p. Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical...
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Springer, 2013. — 340 p. — ISBN: 3642368735, 3642368751 This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation, the KP equation, the nonlinear...
  • №340
  • 3,04 МБ
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New York: Springer, 2017. — 642 p. This book provides explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties, summarizing the author’s works and his joint works with his former students. Further, it presents various oscillator generalizations of the...
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  • 7,75 МБ
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World Scientific Publishing, 2008. — 340 pages. — ISBN: 9812835431. This unique book is designed to provide the reader with an exposition of interesting aspects — encompassing both rudimentary and advanced knowledge — of oscillation theory of partial differential equations, which dates back to the publication in 1955 of a paper by Ph Hartman and A Wintner. The objective of...
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  • 5,11 МБ
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World Scientific Publishing Co. Pte. Ltd., 2006. — 202 p. — ISBN: 981-256-624-4 This is volume one of a two volume series. The intention is to provide a reference book for researchers in nonlinear partial differential equations and nonlinear functional analysis, especially for postgraduate students who want to be led to some of the current research topics. It could be used as a...
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New York: McGrow Hill, 2011. - 250p. Contents : Introduction Classification and characteristics Qualitative behavior of solutions to elliptic equations Qualitative behavior of solutions to evolution equations First-order equations Eigenfunction expansions and integral transforms : theory Eigenfunction expansions and integral transforms : applications Green's...
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Dover, 1987. - 432 pages. This introductory text explores the essentials of partial differential equations applied to common problems in engineering and the physical sciences. It reviews calculus and ordinary differential equations, explores integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory and more. Includes problems and answers.
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Springer, 2017. — 171 p. — (Lecture Notes in Mathematics). — ISBN 10 3319520954. — ISBN 13 978-3319520957. Studying the fine properties of solutions to Stochastic (Partial) Differential Equations with reflection at a boundary, this book begins with a discussion of classical one-dimensional diffusions as the reflecting Brownian motion, devoting a chapter to Bessel processes, and...
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  • 2,64 МБ
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John Wiley & Sons, 1998. — 910 p. — ISBN: 0471315168, 0471612987 The only comprehensive guide to modeling, characterizing, and solving partial differential equations. This classic text by Erich Zauderer provides a comprehensive account of partial differential equations and their applications. Dr. Zauderer develops mathematical models that give rise to partial differential...
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  • 16,49 МБ
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North Holland, 1988. — 242 p. The aim of this book is to provide a comprehensive introduction to the theory of distributions, by the use of solved problems. Although written for mathematicians, it can also be used by a wider audience, including engineers and physicists. The first six chapters deal with the classical theory, with special emphasis on the concrete aspects. The reader...
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Springer International Publishing AG, 2016. — 186 p. — (Lecture Notes in Mathematics 2174) — ISBN: 3319467379 Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov...
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  • 2,22 МБ
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Москва: Издательство иностранной литературы. – 1962. – 208 с. (Библиотека сборника «Математика») Предлагаемая вниманию читателей книга представляет собой перевод статьи трех известных математиков, опубликованной в 1959 г. В этой статье выводятся априорные оценки вблизи границы для решений общих краевых задач для одного эллиптического уравнения с комплексными коэффициентами....
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  • 3,01 МБ
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М.: Наука, 1978. — 352 с. Монография, написанная крупным французским математиком Адамаром, представляет собой классический труд по теории линейных уравнений с частными производными. В книге впервые построено фундаментальное решение линейного гиперболического и эллиптического уравнения второго порядка с переменными коэффициентами. Обсуждается вопрос о принципе Гюйгенса. Общие...
  • №351
  • 4,64 МБ
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М.: Наука, 1978. — 352 с. Монография, написанная крупным французским математиком Адамаром, представляет собой классический труд по теории линейных уравнений с частными производными. В книге впервые построено фундаментальное решение линейного гиперболического и эллиптического уравнения второго порядка с переменными коэффициентами. Обсуждается вопрос о принципе Гюйгенса. Общие...
  • №352
  • 9,92 МБ
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М.: Наука, 1978. — 352 с. Монография, написанная крупным французским математиком Адамаром, представляет собой классический труд по теории линейных уравнений с частными производными. В книге впервые построено фундаментальное решение линейного гиперболического и эллиптического уравнения второго порядка с переменными коэффициентами. Обсуждается вопрос о принципе Гюйгенса. Содержание....
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Ростов н/Д: ЮФУ, 2009. — 80 с. Данное учебное пособие является результатом значительной переработки четырех методических указаний Алексеева А. Д., Радченко Т. Н., Рогожина В. С. и Хасабова Э. Г., опубликованных в УПЛ РГУ в 1992 году. Добавлено много новых задач, приведены подробные решения стандартных задач. Расширена теоретическая часть. Пособие будет полезно при изучении...
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  • 821,21 КБ
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М.: Наука. Гл. ред. физ.-мат. лит., 1991. — 353 с. — (СМБ). Излагается метод численного решения граничных задач, позволяющий получить приближенные решения почти всех классических внутренних и внешних граничных задач математической физики. Метод основан на разложении функции в ряды по фундаментальным решениям (функциям) соответствующих дифференциальных операторов. Исследуются...
  • №355
  • 19,33 МБ
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М.: Наука, 1991. - 352 с. Излагается метод численного решения граничных задач, позволяющий получить приближенные решения почти всех классических внутренних и внешних граничных задач математической физики. Метод основан на разложении функции в ряды по фундаментальным решениям (функциям) соответствующих дифференциальных операторов. Исследуются вопросы универсализации,...
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Мн.: БГУ, 1982. — 208 с., ил. Монография посвящена вопросам теории периодических движений — области, занимающей важное место в общей теории колебаний. Изучаются движения, которые допускают математическое описание с помощью двумерных автономных систем обыкновенных дифференциальных уравнений. Даются методы решения проблемы «центра» и «фокуса». Описываются системы, моделирующие...
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