A remark on two constructions of exponential attractors for \(\alpha\)-contractions
type: Item
instance of: scholarly article
title: A remark on two constructions of exponential attractors for \(\alpha\)-contractions
zbMATH Open document ID: 0898.58035
DOI: 10.1023/A:1022636328133
published in: Journal of Dynamics and Differential Equations
publication date: 1998-11-01T00:00:00Z
review text: This paper proposes an improvement to the original constructions of exponential attractors. An exponential attractor for a continuous map on a compact invariant set \(B\) is a compact, invariant subset \(M\) of \(B\) with finite fractal dimension that contains the global attractor \(A\) which is the \(\omega\)-limit set of \(B\) and attracts all points of \(B\) at a rate which is at least exponential. The authors propose a construction that carries through, even when the invariant set on which the solution semigroup acts is not compact. Their construction requires only that the solution semigroup be \(\alpha\)-contractive and satisfy the discrete squeezing property.
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 1130551
zbMATH Keywords: exponential attractor
zbMATH Keywords: discrete squeezing property
zbMATH Keywords: \(\alpha\)-contractive
author: A. Eden
author: Ciprian Foias
author: V. K. Kalantarov
reviewed by: William J. Satzer Jr.
MaRDI profile type: Publication
Recommended article: Attractivity properties of \(\alpha\)-contractions
Recommended article: Q5090673
Recommended article: Necessary and sufficient conditions for the existence of exponential attractors for semigroups, and applications
Recommended article: Exponential attractors for semigroups in Banach spaces
Recommended article: Fixed point results for \(\{\alpha, \xi\}\)-expansive locally contractive mappings
Recommended article: A construction of a robust family of exponential attractors
Recommended article: On some fixed points of alpha-psi contractive mappings with rational expressions
Recommended article: A note on the Conley attractors of lower semicontinuous multifunctions
Recommended article: \(\alpha\)-contractions and attractors for dissipative semilinear hyperbolic equations and systems
Recommended article: Q5270211
description: scientific article; zbMATH DE number 1130551