On a nonlinear cross diffusion system arising in population dynamics

  1. Gonzalo Galiano 1
  2. María L. Garzón 1
  3. Ansgar Jüngel 2
  1. 1 Departamento de Matemáticas, Universidad de Oviedo
  2. 2 Fachbereich Mathematik und Statistik, Universität Konstanz, Germany
Libro:
XVII Congreso de Ecuaciones Diferenciales y Aplicaciones ; VII Congreso de Matemática Aplicada: Salamanca, 14-28 septiembre 2001
  1. Luis Ferragut (coord.)
  2. Anastasio Santos (coord.)

Editorial: Universidad de Salamanca

ISBN: 8469961446

Año de publicación: 2001

Páginas: 629-630

Congreso: Congreso de Ecuaciones Diferenciales y Aplicaciones (17. 2001. Salamanca)

Tipo: Aportación congreso

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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.

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