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

Galiano, Gonzalo; Garzón, María L.; Jüngel, Ansgar

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

Files

preprint_135.pdf(281.55 KB)

Date

2000

Authors

Galiano, Gonzalo

Garzón, María L.

Jüngel, Ansgar

Series

Konstanzer Schriften in Mathematik und Informatik; 135

Publication type

Preprint

Abstract

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.

Subject (DDC)

004 Computer Science

Cite This

ISO 690

GALIANO, Gonzalo, María L. GARZÓN, Ansgar JÜNGEL, 2000. Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model

BibTex

@unpublished{Galiano2000Semid-6298,
  year={2000},
  title={Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model},
  author={Galiano, Gonzalo and Garzón, María L. and Jüngel, Ansgar}
}

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