February  2005, 12(2): 185-192. doi: 10.3934/dcds.2005.12.185

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

1. 

Department of Mathematics, Hunan Normal University, Changsha, Hunan, China

2. 

Department of Mathematics, The University of Iowa, Iowa City, IA 52242, United States

Received  November 2003 Revised  October 2004 Published  December 2004

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.
Citation: Yi Li, Chunshan Zhao. Global existence of solutions to a cross-diffusion system in higher dimensional domains. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 185-192. doi: 10.3934/dcds.2005.12.185
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