Escher, Joachim; Laurençot, Philippe; Matioc, Bogdan-Vasile
Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media
Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 4 , p. 583-598
Zbl 1227.35177
doi : 10.1016/j.anihpc.2011.04.001
URL stable : http://www.numdam.org/item?id=AIHPC_2011__28_4_583_0

Classification:  35K65,  35K40,  35D30,  35B35,  35Q35
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.

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