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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo

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Volume 1, Issue 3


Volume 13 (2015)

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

Dalibor Pražák
Published Online: 2003-09-01 | DOI: https://doi.org/10.2478/BF02475219


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.

Keywords: global attractor; exponential attractor; fractal dimension; wave equation; nonlinear damping

Keywords: 37L25; 37L30; 35L70

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About the article

Published Online: 2003-09-01

Published in Print: 2003-09-01

Citation Information: Open Mathematics, Volume 1, Issue 3, Pages 411–417, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/BF02475219.

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© 2003 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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