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.
Cite this paper
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