Global Periodic Attractors for a Class of Infinite Dimensional Dissipative Dynamical Systems ()
Affiliation(s)
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.
KEYWORDS
Share and Cite:
Copyright © 2024 by authors and Scientific Research Publishing Inc.
This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.