Volume 48, Number 1, January-February 2014
|Page(s)||231 - 258|
|Published online||10 January 2014|
A hyperbolic model of chemotaxis on a network: a numerical study
1 Istituto per le Applicazioni del Calcolo “M. Picone” –
Consiglio Nazionale delle Ricerche, Via dei Taurini 19, Rome, Italy
2 Laboratoire J.A.Dieudonné, UMR 7351 CNRS, Université Nice Sophia Antipolis, Nice, France
3 Project Team COFFEE, INRIA Sophia-Antipolis, France
Received: 13 June 2012
Revised: 7 May 2013
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.
Mathematics Subject Classification: 65M06 / 35L50 / 92B05 / 92C17 / 92C42
Key words: Hyperbolic system on network / initial-boundary value problem / transmission conditions / asymptotic behavior / finite difference schemes / chemotaxis
© EDP Sciences, SMAI, 2014
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