Abstract
We introduce a numerical scheme to approximate a quasilinear 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 properly handles the presence of vacuum and 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.
Anno
2014
Autori IAC
Tipo pubblicazione
Altri Autori
Natalini, R; Ribot, M ; Twarogowska, M
Editore
International Press,
Rivista
Communications in mathematical sciences