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 satisfies the polynomial growth of arbitrary order and the time-dependent forcing term is only translation-bounded in .