Integrated semigroups and linear partial differential equations with delay
type: Item
instance of: scholarly article
title: Integrated semigroups and linear partial differential equations with delay
zbMATH Open document ID: 1057.34101
author: Cornelia Kaiser
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-06T00:00:00Z
review text: The author studies an equation of the type \[ u'(t)= Au(t)+ \Phi u_t, \quad t\geq 0, \qquad u(0)=x, \quad u_0=f, \tag{1} \] where \(A\) is an (unbounded) operator on a Banach space \(X\), \(\Phi\) is the delay operator, \(u_t\) is the history function and \(x\in X\), \(f\in L^p ([-1,1],Z)\) are the initial values at time 0. Here, \(Z\) is a Banach space such that \(D(A) \hookrightarrow Z\hookrightarrow X\) with continuous embeddings. Using a new perturbation theorem for \(\alpha\)-times integrated semigroup, the author establishes existence results for solutions of the delay equation (1).
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34K06
Mathematics Subject Classification ID: 47D62
Mathematics Subject Classification ID: 35R10
zbMATH DE Number: 2082175
zbMATH Keywords: integrated semigroup
zbMATH Keywords: delay equation
zbMATH Keywords: perturbation
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.10.031
OpenAlex ID: W2082025087
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DOI: 10.1016/J.JMAA.2003.10.031
description: scientific article; zbMATH DE number 2082175