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Zbl 1190.35021
Sun, Jiebao; Wu, Boying; Zhang, Dazhi
Asymptotic behavior of solutions of a periodic diffusion equation. (English)
[J] J. Inequal. Appl. 2010, Article ID 597569, 12 p. (2010). ISSN 1029-242X/e

Summary: We consider a degenerate parabolic equation with logistic periodic sources. First, we establish the existence of nontrivial nonnegative periodic solutions by the monotonicity method. Then, by using the Moser iterative technique and the method of contradiction, we establish the boundedness estimate of nonnegative periodic solutions, by which we show that the attraction of nontrivial nonnegative periodic solutions, that is, all non-trivial nonnegative solutions of the initial boundary value problem, will lie between a minimal and a maximal nonnegative nontrivial periodic solution, as time tends to infinity.

MSC 2000:: *35B10 Periodic solutions of PDE
35K20 Second order parabolic equations, boundary value problems
35K65 Parabolic equations of degenerate type
35K59

Keywords: minimal solution; maximal solution; logistic periodic sources; monotonicity method; Moser iterative technique

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