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Open Mathematics
Article . 2003 . Peer-reviewed
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Open Mathematics
Article . 2003
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Open Mathematics
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A necessary and sufficient condition for the existence of an exponential attractor

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 2003Publisher:Walter de Gruyter GmbHJournal:Open Mathematics, volume 1, pages 411-417 (eissn: 2391-5455, Copyright policy )
Authors: Dalibor Pražák;

doi: 10.2478/bf02475219

A necessary and sufficient condition for the existence of an exponential attractor

Abstract

Abstract We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces. It also captures the quantitative properties of the attractor, i.e., the dimension and the rate of attraction. As an application, we show that the evolution operator for the wave equation with nonlinear damping has an exponential attractor.

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Keywords

fractal dimension, nonlinear damping, exponential attractor, global attractor, 37l30, 35l70, Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems, 37l25, QA1-939, wave equation, Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems, Mathematics, Second-order nonlinear hyperbolic equations

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
18
Average
Top 10%
Average
gold