Geodesic
A hyperbolic model of chemotaxis on a network: a numerical study
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 1, pp. 231-258

Voir la notice de l'article provenant de la source Numdam

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.

DOI : 10.1051/m2an/2013098
Classification : 65M06, 35L50, 92B05, 92C17, 92C42
Keywords: hyperbolic system on network, initial-boundary value problem, transmission conditions, asymptotic behavior, finite difference schemes, chemotaxis 
@article{M2AN_2014__48_1_231_0,
     author = {Bretti, G. and Natalini, R. and Ribot, M.},
     title = {A hyperbolic model of chemotaxis on a network: a numerical study},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {231--258},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {1},
     year = {2014},
     doi = {10.1051/m2an/2013098},
     mrnumber = {3177843},
     zbl = {1285.92004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013098/}
}
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 
PY  - 2014
SP  - 231
EP  - 258
VL  - 48
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013098/
DO  - 10.1051/m2an/2013098
LA  - en
ID  - M2AN_2014__48_1_231_0
ER  - 
%0 Journal Article
%A Bretti, G.
%A Natalini, R.
%A Ribot, M.
%T A hyperbolic model of chemotaxis on a network: a numerical study
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2014
%P 231-258
%V 48
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013098/
%R 10.1051/m2an/2013098
%G en
%F M2AN_2014__48_1_231_0
Bretti, G.; Natalini, R.; Ribot, M. A hyperbolic model of chemotaxis on a network: a numerical study. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 1, pp. 231-258. doi: 10.1051/m2an/2013098

Cité par Sources :