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Numerische Mathematik

, Volume 93, Issue 4, pp 655–673 | Cite as

Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model

  • Gonzalo Galiano
  • María L. Garzón
  • Ansgar Jüngel
Original article

Summary.

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.

Mathematics Subject Classification (1991): 35K55, 65N40. 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Gonzalo Galiano
    • 1
  • María L. Garzón
    • 1
  • Ansgar Jüngel
    • 2
  1. 1.Departamento de Matematicas, Universidad de Oviedo, Avenida de Calvo Sotelo s/n, 33007 Oviedo, Spain (e-mail: {galiano,maria}@orion.ciencias.uniovi.es) ES
  2. 2.Fachbereich Mathematik und Statistik, Universität Konstanz, Fach D193, 78457 Konstanz, Germany (e-mail: juengel@fmi.uni-konstanz.de) DE

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