Invariant manifolds of partial functional differential equations.
type: Item
instance of: scholarly article
title: Invariant manifolds of partial functional differential equations.
zbMATH Open document ID: 1061.34056
author: Nguyen Van Minh
author: Jianhong Wu
published in: Journal of Differential Equations
publication date: 2004-03-29T00:00:00Z
review text: The authors give a proof for the existence and attractivity of center-unstable, center and stable manifolds for general evolutionary processes using the method of graph transforms. They indicate that their results can be applied to a large class of equations generating evolutionary processes that may not be strongly continuous. They then use some classical results on smoothness of invariant manifolds for maps and the technique of ``lifting'' to obtain the smoothness of invariant manifolds. The smoothness result requires the nonlinear perturbation to be \(C^k\)-smooth.
Mathematics Subject Classification ID: 34K19
Mathematics Subject Classification ID: 35K30
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 37L10
zbMATH DE Number: 2062885
zbMATH Keywords: partial functional-differential equation
zbMATH Keywords: evolutionary process
zbMATH Keywords: invariant manifold
zbMATH Keywords: smoothness
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jde.2003.10.006
OpenAlex ID: W1980717747
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DOI: 10.1016/J.JDE.2003.10.006
description: scientific article; zbMATH DE number 2062885