Perturbation and an abstract characterization of evolution semigroups
type: Item
instance of: scholarly article
title: Perturbation and an abstract characterization of evolution semigroups
zbMATH Open document ID: 0884.47017
author: Frank Räbiger
author: A. Rhandi
author: Roland Schnaubelt
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-04-01T00:00:00Z
review text: Evans and Howland used an abstract characterization of evolution semigroups and a perturbation result for \({\mathcal C}_0\) semigroups to treat non-autonomous Schrödinger equations and problems in scattering theory. Here, we proceed in a similar way. At first, we characterize evolution semigroups on spaces of vector-valued functions \(E(X)\) which are induced by a strongly continuous evolution family \((U(t,s))_{t\geq s}\) defined on the Banach space \(X\). From this and a perturbation result of Voigt, we obtain a sufficient condition for an operator on \(L^p(\mathbb{R}, X)\) to be the generator of an evolution semigroup. This will be applied to non-autonomous heat equations with absorption.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 902515
zbMATH Keywords: evolution semigroups
zbMATH Keywords: perturbation result for \({\mathcal C}_ 0\) semigroups
zbMATH Keywords: non-autonomous Schrödinger equations
zbMATH Keywords: scattering theory
zbMATH Keywords: evolution semigroups on spaces of vector-valued functions
zbMATH Keywords: strongly continuous evolution family
zbMATH Keywords: non-autonomous heat equations with absorption
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0096
OpenAlex ID: W1995307167
DOI: 10.1006/JMAA.1996.0096
description: scientific article; zbMATH DE number 902515