Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media

Joachim Escher; Philippe Laurencot; Bogdan-Vasile Matioc

hal-00557791, version 1

Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media

Joachim Escher () ¹, Philippe Laurencot () ², Bogdan-Vasile Matioc () ¹

Annales de l'Institut Henri Poincaré Analyse non linéaire 28 (2011) 583-598

Abstract: We prove global existence of nonnegative weak solutions to a degenerate parabolic system which models the interaction of two thin fluid films in a porous medium. Furthermore, we show that these weak solutions converge at an exponential rate towards flat equilibria.

1: Institute for Applied Mathematics (IFAM)
Leibniz Universität Hannover
2: Institut de Mathématiques de Toulouse (IMT)
Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219

hal-00557791, version 1
http://hal.archives-ouvertes.fr/hal-00557791
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From: Philippe Laurencot <>
Submitted on: Thursday, 20 January 2011 09:25:39
Updated on: Friday, 28 October 2011 08:56:41

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arXiv: 1101.3964

DOI: 10.1016/j.anihpc.2011.04.001

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