Almost Periodic Dynamics of Perturbed Infinite-Dimensional Dynamical Systems
Dynamical Systems
2011-03-15 v1
Abstract
This paper is concerned with the dynamics of an infinite-dimensional gradient system under small almost periodic perturbations. Under the assumption that the original autonomous system has a global attractor given as the union of unstable manifolds of a finite number of hyperbolic equilibrium solutions, we prove that the perturbed non-autonomous system has exactly the same number of almost periodic solutions. As a consequence, the pullback attractor of the perturbed system is given by the union of unstable manifolds of these finitely many almost periodic solutions. An application of the result to the Chafee-Infante equation is discussed.
Cite
@article{arxiv.1103.2371,
title = {Almost Periodic Dynamics of Perturbed Infinite-Dimensional Dynamical Systems},
author = {Bixiang Wang},
journal= {arXiv preprint arXiv:1103.2371},
year = {2011}
}