Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media
Joachim Escher
Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, GermanyPhilippe Laurençot
Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université de Toulouse, F-31062 Toulouse cedex 9, FranceBogdan-Vasile Matioc
Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
![Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-aihpc-volume-28-issue-4.png&w=3840&q=90)
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.
Cite this article
Joachim Escher, Philippe Laurençot, Bogdan-Vasile Matioc, Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 4, pp. 583–598
DOI 10.1016/J.ANIHPC.2011.04.001