Fast reaction limit and long time behavior for a competition-diffusion system with Dirichlet boundary conditions

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July 2007, 8(1): 39-44. doi: 10.3934/dcdsb.2007.8.39

Fast reaction limit and long time behavior for a competition-diffusion system with Dirichlet boundary conditions

E. C.M. Crooks ^1, , E. N. Dancer ^2, and Danielle Hilhorst ^3,

1.	Mathematical Institute, 24-29 St. Giles', Oxford OX1 3LB, United Kingdom
2.	School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia
3.	CNRS and Laboratoire de Mathématiques, Université Paris-Sud 11, Bat. 425, F-91405 Orsay, France

Received November 2005 Revised February 2006 Published April 2007

Abstract
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We consider a two-component competition-diffusion system with equal diffusion coefficients and inhomogeneous Dirichlet boundary conditions. Provided certain conditions on a limit problem hold and provided that the competition rate is sufficiently large, all non-negative solutions of the system converge to a stationary solution of the system as $ t \rightarrow \infty$.

Keywords: boundary-value problem, long-time behaviour, spatial segregation., singular limit, Competition-diffusion system.

Mathematics Subject Classification: 35K50, 35B40, 35K57, 92D2.

Citation: E. C.M. Crooks, E. N. Dancer, Danielle Hilhorst. Fast reaction limit and long time behavior for a competition-diffusion system with Dirichlet boundary conditions. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 39-44. doi: 10.3934/dcdsb.2007.8.39

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