Asymptotic behavior for retarded parabolic equations with superlinear perturbations (Q711713)

A class of nonlinear retarded parabolic equations on a bounded domain with a general linear part given by a positive self-adjoint operator with a compact resolvent and with a time dependent forcing is considered. The nonlinear dependence is allowed to have arbitrary polynomial growth rate. Existence and uniqueness for this class of equations is proved. The asymptotic behavior in time is characterized by proving, under some restrictions on the forcing term, the existence of a pullback attractor in the appropriate functional space.