On long-time dynamics for competition-diffusion systems with inhomogeneous Dirichlet boundary conditions

Details On long-time dynamics for competition-diffusion systems with inhomogeneous Dirichlet boundary conditions On long-time dynamics for competition-diffusion systems with inhomogeneous Dirichlet boundary conditions

2007-07-12

arxiv.org/abs/0707.1771v1

Mathematics

Analysis of PDEs

To appear in Topological Methods in Nonlinear Analysis

Scientific paper

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 freeboundary 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.

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