In this paper, we consider a reaction-diffusion system describing three interacting species in the food chain structure with nonlocal and cross diffusion. We propose a semi-implicit finite volume scheme for this system, we establish existence and uniqueness of the discrete solution, and it is also showed that the discrete solution generated by the given scheme converges to the corresponding weak solution for the model studied. The convergence proof is based on the use of the discrete Sobolev embedding inequalities with general boundary conditions and a space-time compactness argument that mimics the compactness lemma due to Kruzhkov. Finally we give some numerical examples.
DOI : 10.1051/m2an/2014028
Mots-clés : Nonlocal and cross diffusion, food chain model, finite volume scheme
@article{M2AN_2015__49_1_171_0,
author = {Anaya, Ver\'onica and Bendahmane, Mostafa and Sep\'ulveda, Mauricio},
title = {Numerical analysis for a three interacting species model with nonlocal and cross diffusion},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {171--192},
publisher = {EDP-Sciences},
volume = {49},
number = {1},
year = {2015},
doi = {10.1051/m2an/2014028},
mrnumber = {3342196},
zbl = {1314.65115},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2014028/}
}
TY - JOUR AU - Anaya, Verónica AU - Bendahmane, Mostafa AU - Sepúlveda, Mauricio TI - Numerical analysis for a three interacting species model with nonlocal and cross diffusion JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 171 EP - 192 VL - 49 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2014028/ DO - 10.1051/m2an/2014028 LA - en ID - M2AN_2015__49_1_171_0 ER -
%0 Journal Article %A Anaya, Verónica %A Bendahmane, Mostafa %A Sepúlveda, Mauricio %T Numerical analysis for a three interacting species model with nonlocal and cross diffusion %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 171-192 %V 49 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2014028/ %R 10.1051/m2an/2014028 %G en %F M2AN_2015__49_1_171_0
Anaya, Verónica; Bendahmane, Mostafa; Sepúlveda, Mauricio. Numerical analysis for a three interacting species model with nonlocal and cross diffusion. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 1, pp. 171-192. doi : 10.1051/m2an/2014028. http://archive.numdam.org/articles/10.1051/m2an/2014028/
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