Dynamical behavior of nonclassical diffusion equations with memory and lacking instantaneous damping

In this paper, the asymptotic behavior of nonclassical diffusion equations with time-dependent perturbed parameter and lacking instantaneous damping is considered on whole space R-n. The existence and regularity of time-dependent global attractors are proved by using a new analytical technique. It is remarkable that there is not any restriction on the upper growth of the nonlinearity f. The result obtained essentially extends and improves earlier ones.