Geodesic
Existence result for degenerate cross-diffusion system with application to seawater intrusion
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1735-1758

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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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2017058
Classification : 35K65, 35B10, 35D30, 33K40, 35Q35
Keywords: Degenerate parabolic system, entropy estimate, porous medium like systems

Alkhayal, Jana 1 ; Issa, Samar 1 ; Jazar, Mustapha 1 ; Monneau, Régis 1

1 
@article{COCV_2018__24_4_1735_0,
     author = {Alkhayal, Jana and Issa, Samar and Jazar, Mustapha and Monneau, R\'egis},
     title = {Existence result for degenerate cross-diffusion system with application to seawater intrusion},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1735--1758},
     publisher = {EDP-Sciences},
     volume = {24},
     number = {4},
     year = {2018},
     doi = {10.1051/cocv/2017058},
     zbl = {1410.35106},
     mrnumber = {3922430},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017058/}
}
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Alkhayal, Jana; Issa, Samar; Jazar, Mustapha; Monneau, Régis. Existence result for degenerate cross-diffusion system with application to seawater intrusion. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1735-1758. doi: 10.1051/cocv/2017058

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