Fourier parameterization of attractors for dissipative equations in one space dimension
type: Item
instance of: scholarly article
title: Fourier parameterization of attractors for dissipative equations in one space dimension
zbMATH Open document ID: 1041.35018
DOI: 10.1023/B:JODY.0000009744.13730.01
author: Igor Kukavica
published in: Journal of Dynamics and Differential Equations
publication date: 2004-03-15T00:00:00Z
review text: The author considers dissipative equations of the form \[ u_t+(-1)^m u^{(2m)}+ f(x,u,\dots, u^{(2m-1)})= 0 \] and proves that the global attractor is indeed a graph over a sufficiently large number of modes, that is, there exists a spectral projector with finite rank which is one-to-one on the global attractor. The method is based on the fact that for equations of the type \[ V_t- V_{xx}+\beta V_x+ \alpha V= 0 \] there is a change of variables which eliminates the gradient term. A similar fact holds for the equations of order \(2m\).
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 37L25
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35-XX
zbMATH DE Number: 2057859
zbMATH Keywords: determining modes
zbMATH Keywords: Burgers equation
zbMATH Keywords: spectral projector with finite rank
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: b:jody.0000009744.13730.01
OpenAlex ID: W2056534292
description: scientific article; zbMATH DE number 2057859