American Institute of Mathematical Sciences

May  2011, 10(3): 885-915. doi: 10.3934/cpaa.2011.10.885

Robust exponential attractors for non-autonomous equations with memory

 1 Institut für Mathematik, Johann Wolfgang Goethe Universität, D-60054 Frankfurt am Main, Germany 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, China

Received  October 2008 Revised  February 2009 Published  December 2010

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.
Citation: Peter E. Kloeden, José Real, Chunyou Sun. Robust exponential attractors for non-autonomous equations with memory. Communications on Pure & Applied Analysis, 2011, 10 (3) : 885-915. doi: 10.3934/cpaa.2011.10.885
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