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Inertial manifolds and finite-dimensional reduction for dissipative PDEs

Zelik, S (2014) Inertial manifolds and finite-dimensional reduction for dissipative PDEs Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 144 (6). pp. 1245-1327.

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Abstract

This paper is devoted to the problem of finite-dimensional reduction for parabolic partial differential equations. We give a detailed exposition of the classical theory of inertial manifolds as well as various attempts to generalize it based on the so-called Mañé projection theorems. The recent counter-examples showing that the underlying dynamics may in a sense be infinite dimensional if the spectral gap condition is violated, as well as a discussion of the most important open problems, are also included.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Zelik, SUNSPECIFIEDUNSPECIFIED
Date : 1 December 2014
Identification Number : 10.1017/S0308210513000073
Copyright Disclaimer : © 2014 Royal Society of Edinburgh.
Uncontrolled Keywords : Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, REACTION-DIFFUSION SYSTEMS, NAVIER-STOKES EQUATIONS, LIPSCHITZ EMBEDDINGS, DIFFERENTIAL-EQUATIONS, BACKWARD UNIQUENESS, PARABOLIC EQUATIONS, GLOBAL ATTRACTORS, DYNAMICS, COUNTEREXAMPLES, PERSISTENCE
Related URLs :
Additional Information : © 2014 Royal Society of Edinburgh. This is the arXiv version of the paper.
Depositing User : Symplectic Elements
Date Deposited : 23 Feb 2016 10:54
Last Modified : 23 Feb 2016 10:54
URI: http://epubs.surrey.ac.uk/id/eprint/809943

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