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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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