Hausdorff dimension estimation for attractors of nonautonomous dynamical systems in unbounded domains: An example

Abstract

The subject of this paper is the asymptotic behavior of a class of nonautonomous, infinite-dimensional dynamical systems with an underlying unbounded domain. We present an approach that is able to overcome both the law of compactness of the trajectories and the continuity of the spectrum of the linear part of the equations under consideration, providing nevertheless existence of uniform attractors. Moreover, our approach allows us to estimate the Hausdorff dimension of attractors of nonautonomous equations in terms of physical parameters. c 2000 John Wiley & Sons, Inc.