no. 4
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, pp. 583-598

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.

DOI : 10.1016/j.anihpc.2011.04.001
Classification : 35K65, 35K40, 35D30, 35B35, 35Q35
Keywords: Degenerate parabolic system, Weak solutions, Exponential stability, Thin film, Liapunov functional 
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     title = {Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {583--598},
     year = {2011},
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     doi = {10.1016/j.anihpc.2011.04.001},
     zbl = {1227.35177},
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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, pp. 583-598. doi: 10.1016/j.anihpc.2011.04.001

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