Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

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

Pages: 743 - 761, Volume 9, Issue 3/4, May, June 2008      doi:10.3934/dcdsb.2008.9.743

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Chunyou Sun - Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 100080, China (email)
Daomin Cao - Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100080, China (email)
Jinqiao Duan - Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, United States (email)

Abstract: 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, wave equations, critical exponent, asymptotic regularity, uniform attractor.
Mathematics Subject Classification:  35L05, 35B40, 35B41.

Received: January 2007;      Revised: April 2007;      Available Online: February 2008.