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Zbl 0686.35060
Asymptotic behaviour of solutions of periodic competition diffusion system.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 13, No.3, 263-284 (1989). ISSN 0362-546X

In this paper T-periodic solutions of the system $$u\sb t=k\sb 1\Delta u+u(a-bu-cv);\quad v\sb t=k\sb 2\Delta v+v(d-eu-fv)$$ 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.
[C.Bandle]
MSC 2000:
*35K57 Reaction-diffusion equations
35B35 Stability of solutions of PDE
35B50 Maximum principles (PDE)

Keywords: Neumann boundary condition; Existence; uniqueness

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