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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Conti, Monica¹  Pata, Vittorino¹  Temam, Roger² 

[1] Politecn Milan, Dipartimento Matemat F Brioschi, I-20133 Milan, Italy

[2] Indiana Univ, Inst Sci Comp & Appl Math, Bloomington, IN 47405 USA

关键词: Nonautonomous dynamical systems;    Time-dependent attractors;    Wave equation;   

DOI  :  10.1016/j.jde.2013.05.013

来源: Elsevier

【 摘 要 】

For a process U(t, tau):X-tau -> 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, tau) 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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free