The Time-dependent Attractors For The Non-damping Berger Equation With Fading Memory

In this thesis,we investigate the long time behavior of solutions for the nondamping Berger equation with fading memory in the time-dependent space,where the nonlinearity satisfies critical exponential growth.the existence of the timedependent attractor of the non-damping Berger equation with fading memory is proved by using the time-dependent attractor theory proposed by Conti,Plinio,combining with the asymptotic prior estimation and contraction function.This thesis mainly study the two questions as follows:ⅰ)this part study the Berger equation with external force terms that do not explicitly contain time t:where Ω is a bounded domain with a smooth boundary （?）Ω of Rⁿ（n≥5）,k’（s）is the memory kernel function,the time-independent external force term g（x）∈L²（Ω）.ⅱ)this part study the Berger equation with external force terms that do explicitly contain time t:where Ω2 is a bounded domain with a smooth boundary （?）Ω of Rⁿ（n≥）5),k’（s）is the memory kernel function,the time-dependent external force term g（x,t）∈L_loc²(（R;L²（Ω））.