Communications in Mathematical Sciences
Volume 12 (2014)
A well-balanced numerical scheme for a one-dimensional quasilinear hyperbolic model of chemotaxis
Pages: 13 – 39
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 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.
hyperbolic system with source, chemotaxis, stationary solutions with vacuum, finite volume methods, well-balanced scheme
2010 Mathematics Subject Classification
Primary 65M08. Secondary 35L60, 92B05, 92C17.