The method of integrated semigroups for Cauchy problems in Banach spaces
type: Item
instance of: scholarly article
title: The method of integrated semigroups for Cauchy problems in Banach spaces
zbMATH Open document ID: 0920.34054
DOI: 10.1007/BF02674296
published in: Siberian Mathematical Journal
publication date: 1999-05-10T00:00:00Z
review text: The author considers the second-order operator equations \[ u''(t)=Au'(t)+Bu(t), \qquad Qu''(t)=Au'(t)+Bu(t), \] where \(t\geq 0\), \(A\), \(B\), and \(Q\) are linear operators with \(\ker Q\neq\{0\}\) (in other words, the second equation is degenerate). Necessary and sufficient conditions for the well-posedness of the Cauchy problem for these equations are given in the original Banach space and in some subspaces. These conditions are stated in terms of the resolvent \(R(\lambda ^2)=(\lambda ^2-\lambda A -B)^{-1}\) of the operators \(A\) and \(B\).
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 1285615
zbMATH Keywords: second-order operator-differential equation
zbMATH Keywords: Cauchy problem
zbMATH Keywords: correctness
zbMATH Keywords: necessary and sufficient condition
author: I. V. Melnikova
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02674296
OpenAlex ID: W2008812254
description: scientific article; zbMATH DE number 1285615