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            <title xml:lang="en">A SURVEY ON WELL-BALANCED AND ASYMPTOTIC PRESERVING SCHEMES FOR HYPERBOLIC MODELS FOR CHEMOTAXIS</title>
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            <idno type="halRefHtml">&lt;i&gt;ESAIM: Proceedings and Surveys&lt;/i&gt;, 2018, 61, pp.68-92. &lt;a target="_blank" href="https://dx.doi.org/10.1051/proc/201861068"&gt;&amp;#x27E8;10.1051/proc/201861068&amp;#x27E9;&lt;/a&gt;</idno>
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                <title xml:lang="en">A SURVEY ON WELL-BALANCED AND ASYMPTOTIC PRESERVING SCHEMES FOR HYPERBOLIC MODELS FOR CHEMOTAXIS</title>
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              <p>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.</p>
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              <p>Le chimiotactisme est un phénomène biologique largement értudiéces dernières années, aussi bien au niveau biologique que mathématique. De nombreux modèles ont ainsi été proposés, de l’échelle microscopique à l’échelle macroscopique. Dans cet article, nous considérons en particulier deux modèles de type hyperbolique pour la densité d’organismes : un modèle semi-linéaire basé surl’équation de la chaleur hyperbolique (ou équation des ondes dissipatives) et un modèle quasi-léaire basé sur l’équation d’Euler compressible. Ces modèles possèdent des solutions relativement raides et il faut donc utiliser des sch émas de type welb-lalanced et préservant l’asymptotique pour les approcher de façcon précise. Le but de cet article est de présenter différentes techniques de schémas well-balanced et qui préservent l’asymptotique pour les deux modèles hyperboliques de chimiotactisme.</p>
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