Bi-Lipschitz Mane projectors and finite-dimensional reduction for complex Ginzburg-Landau equation
Analysis of PDEs
2021-04-28 v1
Abstract
We present a new method of establishing the finite-dimensionality of limit dynamics (in terms of bi-Lipschitz Mane 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.
Keywords
Cite
@article{arxiv.2002.05053,
title = {Bi-Lipschitz Mane projectors and finite-dimensional reduction for complex Ginzburg-Landau equation},
author = {Anna Kostianko},
journal= {arXiv preprint arXiv:2002.05053},
year = {2021}
}