Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

Singular limit of a two-phase flow problem in porous medium as the air viscosity tends to zero

Pages: 93 - 113, Volume 5, Issue 1, February 2012      doi:10.3934/dcdss.2012.5.93

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Marie Henry - CMI, Université de Provence, 39 rue Frédéric Joliot-Curie 13453 Marseille cedex 13, France (email)
Danielle Hilhorst - CNRS and Laboratoire de Mathématiques, Université de Paris-Sud 11, F-91405 Orsay Cedex, France (email)
Robert Eymard - Université Paris-Est Marne-La-Vallée, 5 bd Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France (email)

Abstract: In this paper we consider a two-phase flow problem in porous media and study its singular limit as the viscosity of the air tends to zero; more precisely, we prove the convergence of subsequences to solutions of a generalized Richards model.

Keywords:  Degenerate parabolic-elliptic system, existence of weak solutions, singular limit, two phase flow in porous media.
Mathematics Subject Classification:  35K65, 35D30, 35B25.

Received: June 2009;      Revised: December 2009;      Available Online: February 2011.