Uniform attractors for non-autonomous wave equations with nonlinear damping

We consider dynamical behavior of non-autonomous wave-type evolutionary equations with nonlinear damping, critical nonlinearity, and time-dependent external forcing which is translation bounded but not translation compact (i.e., external forcing is not necessarily time-periodic, quasi-periodic or almost periodic). A sufficient and necessary condition for the existence of uniform attractors is established using the concept of uniform asymptotic compactness. The required compactness for the existence of uniform attractors is then fulfilled by some new a priori estimates for concrete wave type equations arising from applications. The structure of uniform attractors is obtained by constructing a skew product flow on the extended phase space for the norm-to-weak continuous process.Comment: 33 pages, no figur

Finite-Dimensional Attractors For A General Class Of Nonautonomous Wave Equations

Our aim in this note is to construct attractors and exponential attractors for a general class of nonautonomous semilinear wave equations. Following the approach described in [1], we define a semigroup S(t) associated to an autonomous system, and then prove, using an energy functional, that S(t) is an a-contraction and satisfies the squeezing property. (C) 2000 Elsevier Science Ltd. All rights reserved.WoSScopu