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Bi-Lipschitz Mané projectors and finite-dimensional reduction for complex Ginzburg-Landau equation

Kostianko, Anna (2020) Bi-Lipschitz Mané projectors and finite-dimensional reduction for complex Ginzburg-Landau equation PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES.

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Abstract

We present a new method of establishing the finitedimensionality of limit dynamics (in terms of bi- Lipschitz Mané projectors) for semilinear parabolic systems with cross diffusion terms and illustrate it on the model example of 3D complex Ginzburg- Landau equation with periodic boundary conditions. The method combines the so-called spatial-averaging principle invented by Sell and Mallet-Paret with temporal averaging of rapid oscillations which come from cross-diffusion terms.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Kostianko, Annaa.kostianko@surrey.ac.uk
Date : 13 May 2020
Funders : EPSRC
Grant Title : EPSRC Grant
Copyright Disclaimer : © The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/ by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Uncontrolled Keywords : complex Ginzburg-Landau equation, Lipschitz Mané projectors, inertial manifolds, spatial averaging principle, large dispersion, temporal averaging
Depositing User : James Marshall
Date Deposited : 29 May 2020 14:16
Last Modified : 29 May 2020 14:16
URI: http://epubs.surrey.ac.uk/id/eprint/857009

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