On long-time dynamics for competition-diffusion systems with inhomogeneous Dirichlet boundary conditions
Keywords
Competition-diffusion system, boundary-value problem, singular limit, long-time behaviour, spatial segregationAbstract
We consider a two-component competition-diffusion system with equal diffusion coefficients and inhomogeneous Dirichlet boundary conditions. When the interspecific competition parameter tends to infinity, the system solution converges to that of a free-boundary problem. If all stationary solutions of this limit problem are non-degenerate and if a certain linear combination of the boundary data does not identically vanish, then for sufficiently large interspecific competition, all non-negative solutions of the competition-diffusion system converge to stationary states as time tends to infinity. Such dynamics are much simpler than those found for the corresponding system with either homogeneous Neumann or homogeneous Dirichlet boundary conditions.Downloads
Published
2007-09-01
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CROOKS, Elaine C. M., DANCER, E. Norman and HILHORST, Danielle. On long-time dynamics for competition-diffusion systems with inhomogeneous Dirichlet boundary conditions. Topological Methods in Nonlinear Analysis. Online. 1 September 2007. Vol. 30, no. 1, pp. 1 - 36. [Accessed 26 April 2024].
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