Advances in Pure Mathematics

Volume 3, Issue 5 (August 2013)

ISSN Print: 2160-0368   ISSN Online: 2160-0384

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Global Periodic Attractors for a Class of Infinite Dimensional Dissipative Dynamical Systems

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DOI: 10.4236/apm.2013.35067    3,515 Downloads   5,285 Views  
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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.

Cite this paper

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.

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