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.
@article{bwmeta1.element.doi-10_2478_BF02475219,
author = {Dalibor Pra\v z\'ak},
title = {A necessary and sufficient condition for the existence of an exponential attractor},
journal = {Open Mathematics},
volume = {1},
year = {2003},
pages = {411-417},
zbl = {1030.37053},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475219}
}
Dalibor Pražák. A necessary and sufficient condition for the existence of an exponential attractor. Open Mathematics, Tome 1 (2003) pp. 411-417. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475219/
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