Regular attractors of autonomous and nonautonomous dynamical systems

Abstract

This paper studies regular global attractors of the dynamical systems corresponding to dissipative evolu� tion equations and their nonautonomous perturba� tions. We prove that the nonautonomous dynamical system (process) resulting from a small nonautono� mous perturbation of an autonomous dynamical sys� tem (semigroup) having a regular attractor has a regu� lar nonautonomous attractor as well. Moreover, the symmetric Hausdorff deviation of the perturbed attractors from the unperturbed ones is bounded above by O(e κ ), where e is a perturbation parameter and 0 < κ < 1. We apply the obtained results to weakly dissipa� tive wave equations in a bounded domain in 3 per�