A well-balanced numerical scheme for a one dimensional quasilinear hyperbolic model of chemotaxis

Autor:	Natalini, Roberto, Ribot, Magali, Twarogowska, Monika
Rok vydání:	2012
Předmět:	Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	We introduce a numerical scheme to approximate a quasi-linear hyperbolic system which models the movement of cells under the influence of chemotaxis. Since we expect to find solutions which contain vacuum parts, we propose an upwinding scheme which handles properly the presence of vacuum and, besides, which gives a good approximation of the time asymptotic states of the system. For this scheme we prove some basic analytical properties and study its stability near some of the steady states of the system. Finally, we present some numerical simulations which show the dependence of the asymptotic behavior of the solutions upon the parameters of the system. Comment: 28 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1211.4010 Zobrazit plný text záznamu View this record from Arxiv