Volume 24, Number 4, October–December 2018
|Page(s)||1735 - 1758|
|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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.