Publikation: Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model
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2000
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Galiano, Gonzalo
Garzón, María L.
Jüngel, Ansgar
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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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GALIANO, Gonzalo, María L. GARZÓN, Ansgar JÜNGEL, 2000. Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population modelBibTex
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year={2000},
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<dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
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