Existence of a solution for two phase flow in porous media: The case that the porosity depends on the pressure |
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Authors: | F.Z. Daï m,R. Eymard |
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Affiliation: | a Laboratoire de Mathématique (UMR 8628), Université de Paris-Sud, 91405 Orsay cedex, France b Laboratoire d'Analyse et de Mathématiques Appliquées (UMR 8050), Université de Marne-La-Vallée, 77454 Marne La Vallée cedex, France |
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Abstract: | In this paper we prove the existence of a solution of a coupled system involving a two phase incompressible flow in the ground and the mechanical deformation of the porous medium where the porosity is a function of the global pressure. The model is strongly coupled and involves a nonlinear degenerate parabolic equation. In order to show the existence of a weak solution, we consider a sequence of related uniformly parabolic problems and apply the Schauder fixed point theorem to show that they possess a classical solution. We then prove the relative compactness of sequences of solutions by means of the Fréchet-Kolmogorov theorem; this yields the convergence of a subsequence to a weak solution of the parabolic system. |
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Keywords: | Porous medium Subsidence model Nonlinear parabolic degenerate equations Schauder fixed point theorem Fré chet-Kolmogorov theorem |
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