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

Pages: 39 - 44, Volume 8, Issue 1, July 2007

doi:10.3934/dcdsb.2007.8.39       Abstract        Full Text (123.8K)       Related Articles

E. C.M. Crooks - Mathematical Institute, 24-29 St. Giles', Oxford OX1 3LB, United Kingdom (email)
E. N. Dancer - School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia (email)
Danielle Hilhorst - CNRS and Laboratoire de Mathématiques, Université Paris-Sud 11, Bat. 425, F-91405 Orsay, France (email)

Abstract: 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:  Competition-diffusion system, boundary-value problem, singular limit, long-time behaviour, spatial segregation.
Mathematics Subject Classification:  35K50, 35B40, 35K57, 92D25.

Received: November 2005;      Revised: February 2006;      Published: April 2007.