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)

1 IFAM - Institute for Applied Mathematics
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: degenerate parabolic system; weak solutions; exponential stability; thin film; Liapunov functional

Domaines: Equations aux dérivées partielles [math.AP]

Joachim Escher, Philippe Laurencot, Bogdan-Vasile Matioc. Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2011, 28, pp.583-598. ⟨10.1016/j.anihpc.2011.04.001⟩. ⟨hal-00557791⟩