The Existence Of Periodic Solution And Periodic Attractors For A Class Of Non-autonomous Diffusion Equation

This thesis is concerned with the dynamical behavior of a class of nonclassical diffusion equations u_t -â–³u_t -â–³u + g(u) = f(t) in case f(t) is T-periodic in t. First, the existence of periodic solutions is establishedby using the Galerkin approximation method and Brouwer's fixed point theorem. Second, the existence of periodic uniform forward attrac-tors is investigated. Using the non-compactness measure we first show that the autonomous discrete solution semigroup P_θ(nT) has a global attractor (?)(θ) in the space H²(Ω)∩H₀¹(Ω). Then we show that (?)(θ) is T-periodic inθ. Finally we check the uniform attracting property of {(?)(θ)}_θ∈R , thus proving that {(?)(θ)}_θ∈R is precisely the periodic uniform forward attractors of the original system .