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

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...

Full description

Saved in:
Bibliographic Details
Main Authors Crooks, E. C. M, Dancer, E. N, Hilhorst, D
Format Journal Article
LanguageEnglish
Published 12.07.2007
Subjects
Mathematics - Analysis of PDEs
Online AccessGet full text

Cover

More Information
Summary: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.
DOI:10.48550/arxiv.0707.1771