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

Abstract For a process U ( t , τ ) : X τ → X t 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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