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

Abstract

We introduce a numerical scheme to approximate a quasilinear hyperbolic system which models the movement of cells under the in uence of chemotaxis. Since we expect to find solutions which contain vacuum parts, we proposean upwinding scheme which properly handles the presence of vacuum and whichgives a good approximation of the time asymptotic states of the system. Forthis 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. © 2014 International Press.