Communications on Pure and Applied Analysis (CPAA)

Robust exponential attractors for non-autonomous equations with memory

Pages: 885 - 915, Volume 10, Issue 3, May 2011      doi:10.3934/cpaa.2011.10.885

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Peter E. Kloeden - Institut für Mathematik, Johann Wolfgang Goethe Universität, D-60054 Frankfurt am Main, Germany (email)
José Real - Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain (email)
Chunyou Sun - School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China (email)

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.

Keywords:  Non-autonomous systems with memory, robust exponential attractor, wave equations.
Mathematics Subject Classification:  35L05, 35B40, 35B41.

Received: October 2008;      Revised: February 2009;      Available Online: December 2010.