Continuity of the attractors in time-dependent spaces and applications

In this paper, we investigate the continuity of attractors in time-dependent phase spaces. (i) We establish two abstract criteria on upper semicontinuity and residual pullback D-attractor with respect to perturbations, an equivalence criterion between their equi-attraction, which generalize theory developed recently [27], [28] that (ii) propose notion D-exponential attractor, includes exponential attractor [33] as its spacial case, existence Hölder via quasi-stability method introduced originally by Chueshov Lasiecka [12], [13]. (iii) apply above-mentioned semilinear damped wave equations perturbed speed propagation: ??(t)utt+?ut??u+f(u)=g, perturbation parameter ??(0,1], realize above mentioned D spaces, here allows overcome difficulty hyperbolicity model. These results deepen extend recent spaces literatures [15], [20], [29].