|Publication ahead of print|
|Published online||10 December 2018|
Existence result for degenerate cross-diffusion system with application to seawater intrusion
LaMA-Liban, lebanese university, P.O. Box 37
2 Université Paris-Est, CERMICS, Ecole des Ponts ParisTech, 6 et 8 avenue Blaise Pascal, Cité Descartes Champs-sur-Marne, 77455 Marne-la-vallée Cedex 2, France
* Corresponding author: firstname.lastname@example.org
Accepted: 26 August 2017
In this paper we study a degenerate parabolic system, which is strongly coupled. We prove general existence result, but the uniqueness question remains open. Our proof of existence is based on a crucial entropy estimate which controls the gradient of the solution together with its non-negativity. Our system is of porous medium type which is applicable to models in seawater intrusion.
Mathematics Subject Classification: 35K65 / 35B10 / 35D30 / 33K40 / 35Q35
Key words: Degenerate parabolic system / entropy estimate / porous medium like systems
© EDP Sciences, SMAI 2018
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