In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the behavior of solutions and to discuss the stability and the accuracy of our approximation.
Mots-clés : hyperbolic system on network, initial-boundary value problem, transmission conditions, asymptotic behavior, finite difference schemes, chemotaxis
@article{M2AN_2014__48_1_231_0,
author = {Bretti, G. and Natalini, R. and Ribot, M.},
title = {A hyperbolic model of chemotaxis on a network: a numerical study},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {231--258},
publisher = {EDP-Sciences},
volume = {48},
number = {1},
year = {2014},
doi = {10.1051/m2an/2013098},
mrnumber = {3177843},
zbl = {1285.92004},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2013098/}
}
TY - JOUR AU - Bretti, G. AU - Natalini, R. AU - Ribot, M. TI - A hyperbolic model of chemotaxis on a network: a numerical study JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 231 EP - 258 VL - 48 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2013098/ DO - 10.1051/m2an/2013098 LA - en ID - M2AN_2014__48_1_231_0 ER -
%0 Journal Article %A Bretti, G. %A Natalini, R. %A Ribot, M. %T A hyperbolic model of chemotaxis on a network: a numerical study %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 231-258 %V 48 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2013098/ %R 10.1051/m2an/2013098 %G en %F M2AN_2014__48_1_231_0
Bretti, G.; Natalini, R.; Ribot, M. A hyperbolic model of chemotaxis on a network: a numerical study. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 1, pp. 231-258. doi : 10.1051/m2an/2013098. http://archive.numdam.org/articles/10.1051/m2an/2013098/
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