Communications in Mathematical Sciences

Volume 12 (2014)

Number 3

Rigorous passage to the limit in a system of reaction-diffusion equations towards a system including cross diffusions

Pages: 457 – 472

DOI: http://dx.doi.org/10.4310/CMS.2014.v12.n3.a3

Authors

Fiammetta Conforto (Department of Mathematics and Computer Science, V.le F. Stagno d’Alcontres, Messina, Italy)

Laurent Desvillettes (CMLA, ENS Cachan, CNRS, Cachan, France)

Abstract

We present in this work a rigorous passage to the limit (in Dimension 1) in a system of three reaction-diffusion equations coming out of population dynamics, towards a system of two reaction-diffusion equations, one of which includes a cross diffusion term.

Keywords

cross diffusion, relaxation, SKT model

2010 Mathematics Subject Classification

35B25, 35K57, 35Q92, 92D25

Full Text (PDF format)