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Exponential global attractors for semigroups in metric spaces with applications to differential equations

Published online by Cambridge University Press:  15 March 2011

ALEXANDRE N. CARVALHO  and
JAN W. CHOLEWA
ALEXANDRE N. CARVALHO
Affiliation:
Instituto de Ciências Matemáticas e de Computaçao, Universidade de São Paulo-Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brazil (email: andcarva@icmc.usp.br)
JAN W. CHOLEWA
Affiliation:
Institute of Mathematics, Silesian University, 40-007, Katowice, Poland (email: jcholewa@ux2.math.us.edu.pl)
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Abstract

In this article semigroups in a general metric space V, which have pointwise exponentially attracting local unstable manifolds of compact invariant sets, are considered. We show that under a suitable set of assumptions these semigroups possess strong exponential dissipative properties. In particular, there exists a compact global attractor which exponentially attracts each bounded subset of V. Applications of abstract results to ordinary and partial differential equations are given.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 6 , December 2011 , pp. 1641 - 1667
Copyright
Copyright © Cambridge University Press 2011

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