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

Chunyou Sun; Daomin Cao; Jinqiao Duan

doi:10.3934/dcdsb.2008.9.743

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2008, Volume 9, Issue 3&4: 743-761. Doi: 10.3934/dcdsb.2008.9.743

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

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

Received: December 31, 2006

Revised: March 31, 2007

Published: April 2008

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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.

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Mathematics Subject Classification: 35L05, 35B40, 35B41.

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