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Asymptotic behavior of solutions of a periodic diffusion equation. (English) Zbl 1190.35021
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:
 35B10 Periodic solutions of PDE 35K20 Second order parabolic equations, initial boundary value problems 35K65 Parabolic equations of degenerate type 35K59 Quasilinear parabolic equations
##### References:
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