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

G. Bretti; R. Natalini; M. Ribot

- Volume: 48, Issue: 1, page 231-258
- ISSN: 0764-583X

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topBretti, G., Natalini, R., and Ribot, M.. "A hyperbolic model of chemotaxis on a network: a numerical study." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.1 (2014): 231-258. <http://eudml.org/doc/273258>.

@article{Bretti2014,

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.},

author = {Bretti, G., Natalini, R., Ribot, M.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {hyperbolic system on network; initial-boundary value problem; transmission conditions; asymptotic behavior; finite difference schemes; chemotaxis},

language = {eng},

number = {1},

pages = {231-258},

publisher = {EDP-Sciences},

title = {A hyperbolic model of chemotaxis on a network: a numerical study},

url = {http://eudml.org/doc/273258},

volume = {48},

year = {2014},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 1

SP - 231

EP - 258

AB - 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.

LA - eng

KW - hyperbolic system on network; initial-boundary value problem; transmission conditions; asymptotic behavior; finite difference schemes; chemotaxis

UR - http://eudml.org/doc/273258

ER -

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