Geodesic
A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis
Magali Ribot1
1 Université d’Orléans, CNRS, MAPMO, UMR CNRS 7349, rue de Chartres, Orléans Cedex 2, BP 6759, F-45067 France
ESAIM. Proceedings, Tome 61 (2018), pp. 68-92.

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Chemotaxis is a biological phenomenon widely studied these last years, at the biological level but also at the mathematical level. Various models have been proposed, from microscopic to macroscopic scales. In this article, we consider in particular two hyperbolic models for the density of organisms, a semi-linear system based on the hyperbolic heat equation (or dissipative waves equation) and a quasi-linear system based on incompressible Euler equation. These models possess relatively stiff solutions and well-balanced and asymptotic-preserving schemes are necessary to approximate them accurately. The aim of this article is to present various techniques of well-balanced and asymptotic-preserving schemes for the two hyperbolic models for chemotaxis.
DOI : 10.1051/proc/201861068

Magali Ribot 1

1 Université d’Orléans, CNRS, MAPMO, UMR CNRS 7349, rue de Chartres, Orléans Cedex 2, BP 6759, F-45067 France 
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Magali Ribot. A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis. ESAIM. Proceedings, Tome 61 (2018), pp. 68-92. doi : 10.1051/proc/201861068. http://geodesic.mathdoc.fr/articles/10.1051/proc/201861068/

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