The Existence Of Attractors For Two Classes Of Non-autonomous Dissipative Partial Differential Equations

In this master dissertation, we mainly study the existence of the pull-back D-attractors for weakly damped non-autonomous hyperbolic equations in bounded domains and the uniform attractors for the non-autonomous non-classical diffusion equations with fading memory in unbounded domains.This master dissertation is divided into three sections.In the first section, we introduce some preliminaries knowledge of the research questions.In the second section, we consider the existence of the pullback D-attractors for the following weakly damped non-autonomous hyperbolic equations: where ?(?)Rn is a bounded domain with smooth boundary, ? is a constant. In order to obtain the pullback D-attractors of this dynamical system, we using the D-condition(C).In the third section, we study the existence of the uniform attractors for the following non-autonomous non-classical diffusion equations with fading memory in unbounded domains: where ?> 0.