Perturbation of nilpotent semigroups and application to heat exchanger equations
type: Item
instance of: scholarly article
title: Perturbation of nilpotent semigroups and application to heat exchanger equations
zbMATH Open document ID: 1230.47074
author: Jianhua Chen
author: Wen-Ying Lu
published in: Applied Mathematics Letters
publication date: 2011-07-11T00:00:00Z
review text: The authors describe a stability property for nilpotent semigroups. The main result says that, if \(A\) is the generator of a nilpotent semigroup \(T(t)\) on a Banach space \(X\) and if \(B\) is a closed linear operator in \(X\), then \(A+B\) also generates a nilpotent semigroup \(S(t)\) on \( X\), under some hypotheses on \(B\), which imply that \(B\) is a Miyadera-Voigt perturbation of \(A\). The main idea of the proof is to use the representation of \(S(t)\) as a Dyson-Phillips series and to prove some properties of each term of these series using its integral representation in terms of \(T\) and \(B \). The paper ends with an application of this result to a two-stream parallel-flow heat exchanger equation. The authors prove that the \(C_{0}\)-semigroup generated by the operator associated to this flow is nilpotent and they consider some perturbation of this flow which preserves the nilpotent property of the semigroup.
reviewed by: Alain Brillard
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 47A55
zbMATH DE Number: 5919242
zbMATH Keywords: \(C_{0}\)-semigroup nilpotent
zbMATH Keywords: Miyadera-Voigt perturbation
zbMATH Keywords: Dyson-Phillips series
zbMATH Keywords: heat exchanger equation
MaRDI profile type: Publication
full work available at URL: j.aml.2011.04.023
OpenAlex ID: W2067745237
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DOI: 10.1016/J.AML.2011.04.023
description: scientific article; zbMATH DE number 5919242