Non-autonomous attractors for singularly perturbed parabolic equations on RnRn

We study the asymptotic behavior of solutions of a class of singularly perturbed non-autonomous parabolic equations defined on RnRn with unbounded external terms. We first prove the existence of a pullback attractor for the perturbed equation in L2(Rn)L2(Rn) and then establish the upper semicontinuity of these attractors as small perturbations approach zero. The uniform estimates on the tails of solutions are used to overcome the difficulty caused by the non-compactness of Sobolev embeddings on unbounded domains.