Uniform Attractors for Nonclassical Diffusion Equations with Memory

We introduce a new method (or technique),asymptotic contractive method,to verify uniform asymptotic compactness of a family of processes. after that,the existence and the structure of a compact uniform attractor for the nonautonomous nonclassical diffusion equation with fading memory are proved under the following conditions: the nonlinearity f satisfies the polynomial growth of arbitrary order and the time-dependent forcing term g is only translation-bounded in l l o c 2 (r; l 2 (ω)). � 2016 yongqin xie et al.