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.
A WELL-BALANCED NUMERICAL SCHEME FOR A ONE DIMENSIONAL QUASILINEAR HYPERBOLIC MODEL OF CHEMOTAXIS
Natalini R;Twarogowska M
2014
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
