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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

Chunyou Sun 1, , Daomin Cao 2, and  Jinqiao Duan 3,

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.
Keywords: Non-autonomous systems with memory, critical exponent, uniform attractor., asymptotic regularity, wave equations.
Mathematics Subject Classification: 35L05, 35B40, 35B4.
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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