Non-autonomous wave dynamics with memory --- asymptotic regularity and uniform attractor
Chunyou Sun - Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 100080, China (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
Received: January 2007; Revised: April 2007; Published: February 2008.
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