The $\varepsilon$-entropy of some infinite dimensional compact ellipsoids and fractal dimension of attractors

María Anguiano; Alain Haraux

doi:10.3934/eect.2017018

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2017, Volume 6, Issue 3: 345-356. Doi: 10.3934/eect.2017018

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The $\varepsilon$-entropy of some infinite dimensional compact ellipsoids and fractal dimension of attractors

María Anguiano^1, and
Alain Haraux^2, ,

1.
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, P. O. Box 1160,41080-Sevilla, Spain
2.
CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France

* Corresponding author: Alain Haraux
* Corresponding author: Alain Haraux

Received: March 31, 2017

Revised: April 30, 2017

Published: October 2017

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Abstract

We prove an estimation of the Kolmogorov $\varepsilon$ -entropy in $H$ of the unitary ball in the space $V$ , where $H$ is a Hilbert space and $V$ is a Sobolev-like subspace of $H$ . Then, by means of Zelik's result [7], an estimate of the fractal dimension of the attractors of some nonlinear parabolic equations is established.

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Mathematics Subject Classification: 37L30, 35B41.

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References

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