Global Periodic Attractors for a Class of Infinite Dimensional Dissipative Dynamical Systems ()
ABSTRACT
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.
Share and Cite:
H. Li, "Global Periodic Attractors for a Class of Infinite Dimensional Dissipative Dynamical Systems,"
Advances in Pure Mathematics, Vol. 3 No. 5, 2013, pp. 472-474. doi:
10.4236/apm.2013.35067.
Cited by
No relevant information.