Asymptotic structure of the attractor for processes on time-dependent spaces

We compare the asymptotic structure of the time-dependent attractor A(t) generated by the partial differential equation epsilon u(tt) + alpha u(t) - Delta u + f(u) = g, where the positive function epsilon = epsilon(t) tends to zero as t -> infinity, with the global attractor A(infinity) of its formal limit alpha u(t) - Delta u + f(u) = g. We establish an abstract result and we apply it to the proof of the convergence A(t) -> A(infinity). (C) 2014 Elsevier Ltd. All rights reserved.