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.
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Fatima-Zahra Daim, Robert Eymard, Danielle Hilhorst. Existence of a solution for two phase flow in porous media: The case that the porosity depends on the pressure. Journal of Mathematical Analysis and Applications, Elsevier, 2007, 326 (1), pp.332-351. ⟨10.1016/j.jmaa.2006.02.082⟩. ⟨hal-00693093⟩
