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

E. C.M. Crooks; E. N. Dancer; Danielle Hilhorst

doi:10.3934/dcdsb.2007.8.39

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2007, Volume 8, Issue 1: 39-44. Doi: 10.3934/dcdsb.2007.8.39

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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
2.
School of Mathematics and Statistics, University of Sydney, N.S.W. 2006
3.
CNRS and Laboratoire de Mathématiques, Université Paris-Sud 11, Bat. 425, F-91405 Orsay

Received: October 31, 2005

Revised: January 31, 2006

Published: December 2006

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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$.

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Mathematics Subject Classification: 35K50, 35B40, 35K57, 92D25.

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