A center-stable manifold theorem for differential equations in Banach spaces
type: Item
instance of: scholarly article
title: A center-stable manifold theorem for differential equations in Banach spaces
zbMATH Open document ID: 0776.34051
DOI: 10.1007/BF02098299
published in: Communications in Mathematical Physics
publication date: 1993-06-29T00:00:00Z
review text: The author shows existence (and other properties) of stable center manifolds for the equation \(Z'(t)=Az(t)+f(z(t))\) in a Banach space \(E\) under the following assumptions: (a) \(E=F_ 1\oplus F_ 2\) (topological) with the \(F_ 1\) \(A\)-invariant, and if \(A_ 1\) is the restriction of \(A\) to \(F_ j\), \(A_ 1\) and \(-A_ 2\) generate strongly continuous semigroups, the latter of negative exponential growth. (b) \(f\) is sufficiently smooth with \(f(0)=Df(0)=0\), (c) there is a spectral gap condition and \(F_ 1\) has the \(C^ k\) extension property. There are no applications. The author states that this paper provides the ``mathematical apparatus'' for his paper with \textit{J.-P. Eckmann} [ibid., 221-248 (1993)].
reviewed by: Hector O. Fattorini
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34C30
zbMATH DE Number: 222071
zbMATH Keywords: stable center manifolds
zbMATH Keywords: Banach space
author: Thierry Gallay
MaRDI profile type: Publication
cites work: Q3995079
cites work: Reduction of quasilinear elliptic equations in cylindrical domains with applications
cites work: Propagating fronts and the center manifold theorem
cites work: A reduction principle for nonautonomous systems in infinite-dimensional spaces
cites work: Corrections to: ``Locally invariant manifolds for quasilinear parabolic equations''
cites work: Q4012892
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Q5519417
cites work: Front solutions for the Ginzburg-Landau equation
full work available at URL: https://doi.org/10.1007/bf02098299
OpenAlex ID: W1996529664
description: scientific article; zbMATH DE number 222071