J. K. Hale, “Asymptotic Behavior of Dissipative Systems,” AMS, 1988.

has been cited by the following article:

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

  AUTHORS: Hongyan Li

  KEYWORDS: Dissipative Equation; Global Periodic Attractor; One-Dimensional System

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.5, July 23, 2013

  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.