Non-autonomous attractors for singularly perturbed parabolic equations on \(\mathbb R^n\) (Q708669)

The purpose of this paper is to study asymptotic behavior of solutions to a singularly perturbed non-autonomous parabolic equation \[ \partial_t u +\varepsilon \Delta^2 u - \Delta u = f(x,u) + g(x,t) \] defined on \(\mathbb R^n\) with unbounded external terms. Using uniform estimates on the tails of solutions the authors overcome the difficulty caused by the non-compactness of Sobolev embeddings on unbounded domains. Then the existence of a pullback attractor for the perturbed equation is shown in the phase space \(L^2\). Moreover, they prove the upper semicontinuity of attractors as small parameter \(\varepsilon>0\) tends to zero.