Convergent families of approximate inertial manifolds for nonautonomous evolution equations
type: Item
instance of: scholarly article
title: Convergent families of approximate inertial manifolds for nonautonomous evolution equations
zbMATH Open document ID: 0921.58032
DOI: 10.1007/BF02457751
author: Zongxing Wang
author: Xianling Fan
author: Zhengyou Zhu
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1999-09-30T00:00:00Z
review text: This paper deals with the long time behaviour of non-autonomous infinite-dimensional dynamical systems. Theoretically the inertial manifold cannot be expressed explicitly. To overcome this drawback, the authors construct a convergent family of approximate inertial manifolds \(M_N\), \(N=1,2,\dots\), which can be expressed explicitly. They show that when \(N\to +\infty\), the \(M_N\) approximate the exact inertial manifolds, the existence of which is guaranteed by the spectral gap condition.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1292963
zbMATH Keywords: nonautonomous systems
zbMATH Keywords: long time behaviour
zbMATH Keywords: approximate inertial manifolds
zbMATH Keywords: exact inertial manifolds
zbMATH Keywords: spectral gap condition
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1292963