Slow manifolds for dissipative dynamical systems
type: Item
instance of: scholarly article
title: Slow manifolds for dissipative dynamical systems
zbMATH Open document ID: 1189.34113
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-12-22T00:00:00Z
full work available at URL: http://hdl.handle.net/2097/9168
review text: The author considers the initial value problem \[ \dot u=- Au+ {(Au,u)\over (u,u)},\quad u(0)= u_0\tag{\(*\)} \] in a Hilbert space \(H\) with inner product \((\cdot,\cdot)\), where \(A= A^*\) is a positive self-adjoint operator in \(H\) with spectrum \(\sigma(A)\). He derives conditions on \(\sigma(A)\) such that \((*)\) has a unique global solution \(\widetilde u(t)\) satisfying \(\lim_{t\to\infty}\widetilde u(t)= v\) in the strong sense. If \(v\) is an eigenvector of \(A\) to the smallest eigenvalue of \(A\), then the corresponding eigenspace is called the ``slow'' invariant manifold of \(\dot u=- Au\).
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34C45
zbMATH DE Number: 5651228
zbMATH Keywords: dissipative systems
zbMATH Keywords: dynamical systems
zbMATH Keywords: attractors
zbMATH Keywords: invariant manifolds
zbMATH Keywords: nonlinear evolution
author: A. G. Ramm
MaRDI profile type: Publication
OpenAlex ID: W1980243772
cites work: Invariant manifolds for physical and chemical kinetics
cites work: Q3905908
cites work: Attractors of Strongly Dissipative Systems
cites work: Infinite-dimensional dynamical systems in mechanics and physics.
DOI: 10.1016/J.JMAA.2009.09.049
description: scientific article; zbMATH DE number 5651228