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

G. Bretti; R. Natalini; M. Ribot

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

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

Abstract

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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.

How to cite

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Bretti, 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 -

References

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