# American Institute of Mathematical Sciences

May  2008, 9(3&4, May): 743-761. doi: 10.3934/dcdsb.2008.9.743

## Non-autonomous wave dynamics with memory --- asymptotic regularity and uniform attractor

 1 Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 100080, China 2 Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100080 3 Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616

Received  January 2007 Revised  April 2007 Published  February 2008

The dynamical behavior of non-autonomous strongly damped wave-type evolutionary equations with linear memory, critical nonlinearity, and time-dependent external forcing is investigated. The time-dependent external forcing is assumed to be only translation-bounded, instead of translation-compact. First, the asymptotic regularity of solutions is proved, and then the existence of the compact uniform attractor together with its structure and regularity is obtained.
Citation: Chunyou Sun, Daomin Cao, Jinqiao Duan. Non-autonomous wave dynamics with memory --- asymptotic regularity and uniform attractor. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 743-761. doi: 10.3934/dcdsb.2008.9.743
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