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Existence of a solution for two phase flow in porous media: The case that the porosity depends on the pressure
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 Frechet-Kolmogorov theorem; this yields the convergence of a subsequence to a weak solution of the parabolic system.
Cited literature [8 references]
https://hal-upec-upem.archives-ouvertes.fr/hal-00693093
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Submitted on : Monday, July 31, 2017 - 2:48:17 PM
Last modification on : Thursday, June 17, 2021 - 3:47:15 AM
Contributor : Admin Lama <>
Submitted on : Monday, July 31, 2017 - 2:48:17 PM
Last modification on : Thursday, June 17, 2021 - 3:47:15 AM
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