Asymptotic Behavior of Solutions of a Periodic Diffusion Equation

Asymptotic Behavior of Solutions of a Periodic Diffusion Equation

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We consider a degenerate parabolic equation with logistic periodic sources.First, we establish the existence of nontrivial nonnegative periodic solutions by monotonicity method.Then by using Moser iterative technique Brake Wire 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 Pillowsham Pair boundary value problem, will lie between a minimal and a maximal nonnegative nontrivial periodic solutions, as time tends to infinity.