The Dimension Of The Pullback Attractors For The Reaction-diffusion Equations

In this paper,we consider the dimension of pullback attractors in H01(?)of the following nonautonomous reaction-diffusion equations with the Dirichlet boundary condition in a smooth bounded domain ? C Rn.Firstly,we use the Faedo-Galerkin method to get the existence and unique-ness of solutions.Secondly,in order to get the dimension of pullback attractors in H01(?),we construct a family of sets which satisfies the conditions of existence theorem of the pullback exponential attractors in the Banach space under the as-sumption that ?-?te?1?||g(?,x)||L22(?_d?<?,t ?R,and prove the existence of the reaction-diffusion equations pullback exponential attractors.The same assump-tions guarantee also the existence of the pullback global attractor with uniformly bounded fractal dimension.