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, Volume 28 (2011) no. 4, p. 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 : https://doi.org/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
@article{AIHPC_2011__28_4_583_0,
author = {Escher, Joachim and Lauren\c cot, Philippe and Matioc, Bogdan-Vasile},
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},
publisher = {Elsevier},
volume = {28},
number = {4},
year = {2011},
pages = {583-598},
doi = {10.1016/j.anihpc.2011.04.001},
zbl = {1227.35177},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2011__28_4_583_0}
}

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, Volume 28 (2011) no. 4, pp. 583-598. doi : 10.1016/j.anihpc.2011.04.001. http://www.numdam.org/item/AIHPC_2011__28_4_583_0/

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