Differentiability and growth bounds of solutions of delay equations
type: Item
instance of: scholarly article
title: Differentiability and growth bounds of solutions of delay equations
zbMATH Open document ID: 1080.34061
author: Charles J. K. Batty
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-03-08T00:00:00Z
review text: This paper deals with the eventual differentiability of the semigroup solution for the following delay equation in Banach spaces \[ u'(t)=Au(t)+\mu u_t, t\geq0, \quad u_0=\varphi \in C([-1,0];X), \] where \(A\) generates an immediatly norm-continuous semigroup on a Banach space \(X\), \(C([-1,0];X)\) is the space of continuous functions from \([-1,0]\) to \(X\) endowed with the uniform norm topology and \(\mu\) is a bounded linear operator from \(C([-1,0];X)\) to \(X\). The history function is defined by \(u_t(\alpha)=u(t+\alpha),\) \(\alpha \in [-1,0]\). The eventual differentability is obtained by the rate of decay of the resolvent of \(A\) along vertical lines.
reviewed by: Khalil Ezzinbi
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34K06
Mathematics Subject Classification ID: 34K12
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 2141772
zbMATH Keywords: semigroup
zbMATH Keywords: growth bound
zbMATH Keywords: resolvent
zbMATH Keywords: delay equations
zbMATH Keywords: eventually differentiable
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.04.063
OpenAlex ID: W2085025207
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DOI: 10.1016/J.JMAA.2004.04.063
description: scientific article; zbMATH DE number 2141772