A dissertation in mathematics. Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy — 2009. — 67 p.The mathematical modeling and analysis of non-linear flows in porous media is quickly becoming a key to solving many challenging problems in engineering and applied sciences. Most studies in porous media are based on Darcy’s law so “Darcy’s equation has become the model of choice for the study of the flow of fluids through porous solids due to pressure gradients, so much that it has now been elevated to the status of a law in physics” as mentioned in . Darcy’s law is a phenomenologically derived constitutive equation that describes the flow of a fluid through a porous medium as a linear relationship between the pressure gradient and the fluid velocity. The law was formulated by Henry Darcy based on the results of experiments () on the flow of water through beds of sand.
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