Finite-dimensional attractors for a general class of nonautonomous wave equations
type: Item
instance of: scholarly article
title: Finite-dimensional attractors for a general class of nonautonomous wave equations
zbMATH Open document ID: 0985.37090
DOI: 10.1016/S0893-9659(00)00027-6
published in: Applied Mathematics Letters
publication date: 2000-11-16T00:00:00Z
review text: The authors deal with a large-time asymptotic of a general nonautonomous wave equation of the form \[ Pu''+ Qu'+ Au+ F(t, u)= h(t) \] in a Hilbert space \(H\), where \(A\), \(P\), and \(Q\) are linear positive selfadjoint operators. Under some general conditions the authors prove the existence of an exponential attractor and as a consequence obtain a global finite-dimensional attractor. To this end they use that the corresponding ``semigroup'' \(S(t)\) is an \(\alpha\)-contraction and verify the squeezing property.
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B41
zbMATH DE Number: 1531170
zbMATH Keywords: finite-dimensional attractors
zbMATH Keywords: nonautonomous wave equations
zbMATH Keywords: squeezing property
author: A. Eden
author: V. K. Kalantarov
author: Alain Miranville
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Attractors of non-autonomous dynamical systems and their dimension
cites work: Q4851736
cites work: Q4716803
cites work: Uniform inertial sets for damped wave equations
cites work: Infinite-dimensional dynamical systems in mechanics and physics
cites work: Decay estimates for the generalized damped extensible string and beam equations
cites work: Q5584121
cites work: Global attractors and approximate inertial
cites work: Q4039920
cites work: Exponential attractors for nonautonomous evolution equations
cites work: Exponential attractors for nonautonomous first-order evolution equations
full work available at URL: s0893-9659(00)00027-6
OpenAlex ID: W2053714135
description: scientific article; zbMATH DE number 1531170