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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 \[ u_ t=k_ 1\Delta u+u(a-bu-cv);\quad v_ t=k_ 2\Delta v+v(d-eu-fv) \] in \(\Omega\) \(\times (-\infty,\infty)\) 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:

35K57 Reaction-diffusion equations
35B35 Stability in context of PDEs
35B50 Maximum principles in context of PDEs
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