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

Gabriella Bretti (1) , Roberto Natalini (1) , Magali Ribot (2, 3)

1 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 COFFEE - COmplex Flows For Energy and Environment

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

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Gabriella Bretti, Roberto Natalini, Magali Ribot. A hyperbolic model of chemotaxis on a network: a numerical study. ESAIM: Mathematical Modelling and Numerical Analysis, 2014, 48 (1), pp.231-258. ⟨hal-00763886⟩