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

@inproceedings{Natalini2012AWN,
title={A well-balanced numerical scheme for a one dimensional quasilinear hyperbolic model of chemotaxis},
author={Roberto Natalini and Magali Ribot and Monika Twarogowska},
year={2012}
}

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… CONTINUE READING