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A hyperbolic model of chemotaxis on a network: a numerical study

Published online by Cambridge University Press:  10 January 2014

G. Bretti ,
R. Natalini  and
M. Ribot
G. Bretti
Affiliation:
Istituto per le Applicazioni del Calcolo “M. Picone” – Consiglio Nazionale delle Ricerche, Via dei Taurini 19, Rome, Italy. g.bretti@iac.cnr.it; roberto.natalini@cnr.it
R. Natalini
Affiliation:
Istituto per le Applicazioni del Calcolo “M. Picone” – Consiglio Nazionale delle Ricerche, Via dei Taurini 19, Rome, Italy. g.bretti@iac.cnr.it; roberto.natalini@cnr.it
M. Ribot
Affiliation:
Laboratoire J.A.Dieudonné, UMR 7351 CNRS, Université Nice Sophia Antipolis, Nice, France; ribot@unice.fr Project Team COFFEE, INRIA Sophia-Antipolis, France
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Abstract

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.

Keywords

Hyperbolic system on networkinitial-boundary value problemtransmission conditionsasymptotic behaviorfinite difference schemeschemotaxis
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 1 , January 2014 , pp. 231 - 258
Copyright
© EDP Sciences, SMAI, 2014

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