Pullback attractors for a class of non-autonomous semilinear parabolic equations with infinite delay

Abstract

We study the existence, uniqueness and the asymptotic behavior of solutions of a class of retarded non-autonomous semilinear parabolic equations with infinite delay effects in the weighted space Cγ, nonlinearity containing supelinear perturbations, and time-dependent external forces. With a suitable exponential growth of the external force, we prove the existence of pullback attractors without restriction on the growth order of polynomial type nonlinearity.