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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.
35B10Periodic solutions of PDE
35K20Second order parabolic equations, initial boundary value problems
35K65Parabolic equations of degenerate type
35K59Quasilinear parabolic equations