Robust exponential attractors for non-autonomous equations with memory

Peter E. Kloeden; José Real; Chunyou Sun

doi:10.3934/cpaa.2011.10.885

Article Contents

2011, Volume 10, Issue 3: 885-915. Doi: 10.3934/cpaa.2011.10.885

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Robust exponential attractors for non-autonomous equations with memory

1.
Institut für Mathematik, Johann Wolfgang Goethe Universität, D-60054 Frankfurt am Main
2.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla
3.
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000

Received: September 30, 2008

Revised: January 31, 2009

Published: April 2011

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Abstract

The aim of this paper is to consider the robustness of exponential attractors for non-autonomous dynamical systems with line memory which is expressed through convolution integrals. Some properties useful for dealing with the memory term for non-autonomous case are presented. Then, we illustrate the abstract results by applying them to the non-autonomous strongly damped wave equations with linear memory and critical nonlinearity.

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Mathematics Subject Classification: 35L05, 35B40, 35B41.

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