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

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

Published:2020-07 Issue:2239 Volume:476 Page:20200144
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Kostianko Anna¹²^ORCID

Affiliation:

1. University of Surrey, Department of Mathematics, Guildford, Surrey GU2 7XH, UK

2. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People’s Republic of China

Abstract

We present a new method of establishing the finite-dimensionality 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 three-dimensional 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.

Funder

Engineering and Physical Sciences Research Council

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2020.0144

Reference30 articles.

1. Miranville A Zelik S. 2008 Attractors for dissipative partial differential equations in bounded and unbounded domains. In Handbook of differential equations: evolutionary equations (eds CM Dafermos M Pokorny) vol. 4 pp. 103–200. Amsterdam The Netherlands: Elsevier/North Holland.

2. Dynamics of Evolutionary Equations

3. Temam R. 1997 Infinite-dimensional dynamical systems in mechanics and physics . Applied Mathematical Sciences vol. 68. New York NY: Springer.

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