# American Institute of Mathematical Sciences

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

 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

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 $t \rightarrow \infty$.
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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