Global existence of solutions to a cross-diffusion system in higher dimensional domains

Yi Li; Chunshan Zhao

doi:10.3934/dcds.2005.12.185

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2005, Volume 12, Issue 2: 185-192. Doi: 10.3934/dcds.2005.12.185

This issue Previous Article Next Article Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations

Global existence of solutions to a cross-diffusion system in higher dimensional domains

Yi Li^1, and
Chunshan Zhao^2,

1.
Department of Mathematics, Hunan Normal University, Changsha, Hunan
2.
Department of Mathematics, The University of Iowa, Iowa City, IA 52242

Received: October 31, 2003

Revised: September 30, 2004

Published: January 2005

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Abstract

We consider a strongly coupled nonlinear parabolic system which arises from population dynamics in $N$-dimensional $(N\geq 1)$ domains. We establish global existence of classical solutions under certain restrictions on diffusion coefficients, self-diffusion coefficients and cross-diffusion coefficients for both species.

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Mathematics Subject Classification: 35K55, 35B45, 35K50, 35K60, 35K57, 92B05, 92D25.

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