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Abstract: We consider a two-component competition-diffusion system with equal diffusioncoefficients and inhomogeneous Dirichlet boundary conditions. When theinterspecific competition parameter tends to infinity, the system solutionconverges to that of a freeboundary problem. If all stationary solutions ofthis limit problem are non-degenerate and if a certain linear combination ofthe boundary data does not identically vanish, then for sufficiently largeinterspecific competition, all non-negative solutions of thecompetition-diffusion system converge to stationary states as time tends toinfinity. Such dynamics are much simpler than those found for the correspondingsystem with either homogeneous Neumann or homogeneous Dirichlet boundaryconditions.



Author: E.C.M. Crooks, E.N. Dancer, D. Hilhorst

Source: https://arxiv.org/







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