Vv. Chepyzhov et Ma. Efendiev, Hausdorff dimension estimation for attractors of nonautonomous dynamical systems in unbounded domains: An example, COM PA MATH, 53(5), 2000, pp. 647-665
The subject of this paper is the asymptotic behavior of a class of nonauton
omous, infinite-dimensional dynamical systems with an underlying unbounded
domain. We present an approach that is able to overcome both the law of com
pactness of the trajectories and the continuity of the spectrum of the line
ar part of the equations under consideration, providing nevertheless existe
nce of uniform attractors. Moreover, our approach allows us to estimate the
Hausdorff dimension of attractors of nonautonomous equations in terms of p
hysical parameters. (C) 2000 John Wiley & Sons, Inc.