A hyperbolic model of chemotaxis on a network: a numerical study
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 1, p. 231-258

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.

DOI : https://doi.org/10.1051/m2an/2013098
Classification:  65M06,  35L50,  92B05,  92C17,  92C42
Keywords: 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, Roberto and Ribot, M.},
title = {A hyperbolic model of chemotaxis on a network: a numerical study},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {48},
number = {1},
year = {2014},
pages = {231-258},
doi = {10.1051/m2an/2013098},
zbl = {1285.92004},
mrnumber = {3177843},
language = {en},
url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 1, pp. 231-258. doi : 10.1051/m2an/2013098. http://www.numdam.org/item/M2AN_2014__48_1_231_0/

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