Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model |
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Authors: | Gonzalo Galiano María L Garzón Ansgar Jüngel |
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Institution: | 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.Fachbereich Mathematik und Statistik, Universit?t Konstanz, Fach D193, 78457 Konstanz, Germany (e-mail: juengel@fmi.uni-konstanz.de)
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Abstract: | 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.
Received September 10, 2001 / Revised version received February 25, 2002 / Published online June 17, 2002 |
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Keywords: | Mathematics Subject Classification (1991): 35K55 65N40 |
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