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In this paper we consider the
existence of a global periodic attractor for a class of infinite dimensional
dissipative equations under homogeneous Dirichlet boundary conditions. It is
proved that in a certain parameter, for an arbitrary timeperiodic driving
force, the system has a unique periodic solution attracting any bounded set
exponentially in the phase space, which implies that the system behaves exactly
as a one-dimensional system. We mention, in particular, that the obtained
result can be used to prove the existence of the global periodic attractor for
abstract parabolic problems.
In this paper, we study the existence of exponential attractors for strongly damped wave equations with a time-dependent driving force. To this end, the uniform H?lder continuity is established to the variation of the process in the phase apace. In a certain parameter region, the exponential attractor is a uniformly exponentially attracting time-dependent set in the phase apace, and is finite-dimensional no matter how complex the dependence of the external forces on time is. On this basis, we also obtain the existence of the infinite-dimensional uniform exponential attractor for the system.