Uniform attractors for non-autonomous wave equations with nonlinear damping

Details Uniform attractors for non-autonomous wave equations with nonlinear damping Uniform attractors for non-autonomous wave equations with nonlinear damping

2006-06-30

arxiv.org/abs/math/0606776v1

Mathematics

Dynamical Systems

33 pages, no figure

Scientific paper

10.1137/060663805

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.

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