Existence And Regularity Of Time-dependent Attractors For Nonlinear Evolution Equations

In this master dissertation, based on a new theory of time-dependent global at-tractors introduced by Conti etc., we study the following nonlinear evolution equa-tions We prove the existence and regularity of time-dependent global attractors by using the energy estimation as well as the operator decomposion technique, where Ω(?) R~N(N≥3) is a bounded domain with smooth boundary (?)Ω,u=u(x,t): Ω→R is a unknown function, g∈L~2(Ω),ε(t)> 0 is a positive decreasing function of time vanishing at infinity.Besides, we investigate the existence of attractors for the nonlinear evolution equations with nonlinear damping on time-dependent space in line with the con-tractive function method. where Ω(?)R~N (N≥3) is a bounded domain with smooth boundary (?)Ω,u=u(x,t): Ω→R is a unknown function,h∈L~2(Ω),f,g∈C~1(R).