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

Pages: 185 - 192, Volume 12, Issue 2, February 2005

doi:10.3934/dcds.2005.12.185       Abstract        Full Text (190.8K)       Related Articles

Yi Li - Department of Mathematics, Hunan Normal University, Changsha, Hunan, China (email)
Chunshan Zhao - Department of Mathematics, The University of Iowa, Iowa City, IA 52242, United States (email)

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.

Keywords:  Global existence, cross-diffusion, self-diffusion, nonlinear parabolic system, population dynamics, Shigesada-Kawasaki-Teramoto model.
Mathematics Subject Classification:  35K55, 35B45, 35K50, 35K60, 35K57, 92B05, 92D25.

Received: November 2003;      Revised: October 2004;      Published: December 2004.