Upper semicontinuity of pullback attractors for nonclassical diffusion equations

Our aim in this paper is to study the long time behavior, in terms of upper semi-continuous property of pullback attractors, of nonclassical diffusion equations with nonautonomous perturbation. Specifically, we prove that, under some proper assumptions, the pullback attractor {A(g)(t)}(t is an element of R) of Eq. (1) and the global attractor A of Eq. (1) with epsilon = 0 satisfy lim dist(X) (A(epsilon)(t), A) = 0 for any t is an element of R. (C) 2010 American epsilon -> 0(+) Institute of Physics. [doi: 10.1063/1.3277152]