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Asymptotic behaviour of solutions of periodic competition diffusion system. (English) Zbl 0686.35060

In this paper T-periodic solutions of the system

u t =k 1 Δu+u(a-bu-cv);v t =k 2 Δv+v(d-eu-fv)

in Ω ×(-,) are studied which satisfy a Neumann boundary condition. It is assumed that the coefficients are T-periodic and depend also on the space variable. Existence, uniqueness and stability results are established. The techniques rely on monotonicity methods and on the generalized maximum principle. This paper extends previous work of the second author.

Reviewer: C.Bandle

MSC:
35K57Reaction-diffusion equations
35B35Stability of solutions of PDE
35B50Maximum principles (PDE)