Existence result for degenerate cross-diffusion system with application to seawater intrusion

Alkhayal, Jana; Issa, Samar; Jazar, Mustapha; Monneau, Régis

ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1735-1758.

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.

Classification : 35K65, 35B10, 35D30, 33K40, 35Q35
Mots clés : Degenerate parabolic system, entropy estimate, porous medium like systems

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