Uniform attractors for nonclassical diffusion equations with memory (Q301503)

Summary: 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 \(L_{\operatorname{loc}}^2(\mathbb R; L^2(\Omega))\).