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

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

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. Ou...

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Veröffentlicht in:ESAIM. Control, optimisation and calculus of variations optimisation and calculus of variations, 2018-10, Vol.24 (4), p.1735-1758
Hauptverfasser: Alkhayal, Jana, Issa, Samar, Jazar, Mustapha, Monneau, Régis
Format: Artikel
Sprache:eng
Schlagworte:
33K40
35B10
35D30
35K65
35Q35
Degenerate parabolic system
Entropy
entropy estimate
Mathematical analysis
Porous media
porous medium like systems
Salt water intrusion
Seawater
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Beschreibung
Zusammenfassung: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.
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2017058