The Time-dependent Attractors For Non-damping Abstract Evolution Equations With Fading Memory

In this thesis,we study the time-dependent long-time dynamics of the non-damping evolution equation with fading memory under Dirichlet boundary condition,where the nonlinearity satisfies critical growth.By applying the modified pullback attrac-tors theory,asymptotic a priori estimate method and operator decomposition technique,the existence and regularity of time-dependent attractors for the non-damping abstract evolution equations with fading memory are proved.This thesis includes four chapters:In chapter one,we first introduce the developing process and backgrounds of infinite-dimensional dynamical systems,and the basic theory development and the research pro-cess of time-dependent attractors.Then,we put forward the main problem.In chapter two,some preparations are presented,including spaces and some notations for the non-damping abstract evolution equation with fading memory,preparation for the article and some abstract results.In chapter three,the existence and regularity of time-dependent attractor in weak topological spaces H l?=V?+?×V?×L?2(R+;V?+?)for the non-damping abstract evolution equation with fading memory are proved,where the nonlinearity satisfies critical growth and the external forcing term only belongs to V-??In chapter four,the existence and regularity of time-dependent attractor in strong topological spaces H l?+?=V2?+?×V?+?×L?2(R+;V2?+?)(strong time-dependent attractor)for the non-damping abstract evolution equation with fading memory are proved,where the nonlinearity satisfies critical growth and the external forcing term belongs to H.