ANZIAM J.
45 (2003), 207-222
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The dimension of attractors of nonautonomous partial differential equations
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T. Caraballo
Dpto. Ecuaciones Diferenciales y Análisis Numérico
Universidad de Sevilla
Apdo. de Correos 1160
41080-Sevilla
Spain
caraball@us.es
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J. A. Langa
Dpto. Ecuaciones Diferenciales y Análisis Numérico
Universidad de Sevilla
Apdo. de Correos 1160
41080-Sevilla
Spain
langa@numer.us.es
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J. Valero
Universidad Cardenal Herrera CEU
Comisario 3
03203 Elche
Alicante
Spain
valer.el@ceu.es
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Abstract
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The concept of nonautonomous (or cocycle)
attractors has become a proper tool for the study
of the asymptotic behaviour of general
nonautonomous partial differential equations.
This is a time-dependent family of compact sets,
invariant for the associated process and
attracting
``from  ''. In general, the concept is rather different
to the classical global attractor for autonomous
dynamical systems. We prove a general result on
the finite fractal dimensionality of each compact
set of this family. In this way, we generalise
some previous results of Chepyzhov and Vishik.
Our results are also applied to differential
equations with a nonlinear term having polynomial
growth at most.
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