# American Institute of Mathematical Sciences

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