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Counterexamples to the regularity of Mane projections and global attractors

Eden, A, Kalanarov, V and Zelik, S (2011) Counterexamples to the regularity of Mane projections and global attractors arXiv.

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Abstract

We study the global attractors of abstract semilinear parabolic equations and their projections to finite-dimensional planes. It is well-known that the attractor can be embedded into the finite-dimensional inertial manifold if the so-called spectral gap condition is satisfied. We show that in the case when the spectral gap condition is violated, it is possible to construct the nonlinearity in such way that the corresponding attractor cannot be embedded into any finite-dimensional Log-Lipschitz manifold and, therefore, does not possess any Mane projections with Log-Lipschitz inverse. In addition, we give an example of finitely smooth nonlinearity such that the attractor has finite Hausdorff but infinite fractal dimension.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Eden, AUNSPECIFIEDUNSPECIFIED
Kalanarov, VUNSPECIFIEDUNSPECIFIED
Zelik, SUNSPECIFIEDUNSPECIFIED
Date : 1 August 2011
Related URLs :
Additional Information : This is an arXiv version of the paper.
Depositing User : Symplectic Elements
Date Deposited : 26 Aug 2015 17:39
Last Modified : 26 Aug 2015 17:39
URI: http://epubs.surrey.ac.uk/id/eprint/806848

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