On a nonlinear cross diffusion system arising in population dynamics

Gonzalo Galiano ^[1] ; María L. Garzón ^[1] ; Ansgar Jüngel ^[2]
1. [1] Universidad de Oviedo
  
  Universidad de Oviedo
  
  Oviedo, España
2. [2] University of Konstanz
  
  University of Konstanz
  
  Landkreis Konstanz, Alemania
Localización: XVII Congreso de Ecuaciones Diferenciales y Aplicaciones ; VII Congreso de Matemática Aplicada: Salamanca, 14-28 septiembre 2001 / coord. por Luis Ferragut Canals , Anastasio Pedro Santos Yanguas , 2001, ISBN 8469961446, págs. 629-630
Idioma: inglés
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Resumen
- A positivity-preserving numerical scheme for a strongly coupled cross-diffusion model for two competing species is presented, based on a semi-discretization in time. The variables are the population densities of the species. Existence of strictly positive weak solutions to the semidiscrete problem is proved. Moreover, it is shown that the semidiscrete solutions converge to a non-negative solution of the continuous system in one space dimension. The proofs are based on a symmetrization of the problem via an exponential transformation of variables and the use of an entropy functional.