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Attractors for processes on time-dependent spaces. Applications to wave equations

Authors
Journal
Journal of Differential Equations
0022-0396
Publisher
Elsevier
Publication Date
Volume
255
Issue
6
Identifiers
DOI: 10.1016/j.jde.2013.05.013
Keywords
  • Nonautonomous Dynamical Systems
  • Time-Dependent Attractors
  • Wave Equation

Abstract

Abstract For a process U(t,τ):Xτ→Xt acting on a one-parameter family of normed spaces, we present a notion of time-dependent attractor based only on the minimality with respect to the pullback attraction property. Such an attractor is shown to be invariant whenever U(t,τ) is T-closed for some T>0, a much weaker property than continuity (defined in the text). As a byproduct, we generalize the recent theory of attractors in time-dependent spaces developed in Di Plinio et al. (2011) [13]. Finally, we exploit the new framework to study the longterm behavior of wave equations with time-dependent speed of propagation.

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