Formule de Duhamel abstraite. (Abstract Duhamel formula)
type: Item
instance of: scholarly article
title: Formule de Duhamel abstraite. (Abstract Duhamel formula)
zbMATH Open document ID: 0555.35058
DOI: 10.1007/BF01193611
author: R. M. Dubois
author: Günter Lumer
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: The authors give a rigorous proof of the Duhamel principle, in a general framework that includes, in particular, the elliptic operators with continuous coefficients. Consider an abstract problem of the following type: \((*)\quad \mu '=Au;\quad \mu (0)=u_ 0;\quad Bu=g,\) where A is a linear operator in a Banach space X, B is a linear operator from X into a Banach space Y and \(u_ 0\in X\) is an initial condition. They find some conditions in order to have (formally) \(\mu (t)=(d/dt)\int^{t}_{0}\mu (s,t-s)ds\) where \(\mu(s,\cdot)\) is the solution of (*) corresponding to \(g(s)\in Y\), when s is hold fixed (i.e. with time-independent constraints).
reviewed by: Elvira Mascolo
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 3884610
zbMATH Keywords: Duhamel principle
zbMATH Keywords: continuous coefficients
zbMATH Keywords: abstract problem
MaRDI profile type: Publication
cites work: Q4186888
full work available at URL: https://doi.org/10.1007/bf01193611
OpenAlex ID: W2080425283
description: scientific article; zbMATH DE number 3884610