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De Carvalho, Alexandre Nolasco; Sonner, Stefanie

Pullback exponential attractors for evolution processes in Banach spaces: properties and applications. (English) Zbl 1336.37059

Commun. Pure Appl. Anal. 13, No. 3, 1141-1165 (2014).
Authors’ abstract: This article is a continuation of our previous work [A. N. De Carvalho and S. Sonner, Commun. Pure Appl. Anal. 12, No. 6, 3047–3071 (2013; Zbl 1390.37126)], where we formulated general existence theorems for pullback exponential attractors for asymptotically compact evolution processes in Banach spaces and discussed its implications in the autonomous case. We now study properties of the attractors and use our theoretical results to prove the existence of pullback exponential attractors in two examples, where previous results do not apply.
Reviewer: Ahmad Abdullah (Amman)

Cited in 28 Documents

MSC:

37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems
37B55 Topological dynamics of nonautonomous systems
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
37B40 Topological entropy

Keywords:

exponential attractors; non-autonomous dynamical systems; pullback and forwards attractors; non-autonomous Chafee-Infante equation; non-autonomous damped wave equation

Citations:

Zbl 1390.37126
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Full Text: DOI Link

References:

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