On dissipative wave equations in Hilbert space
type: Item
instance of: scholarly article
title: On dissipative wave equations in Hilbert space
zbMATH Open document ID: 0833.34053
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-09-08T00:00:00Z
review text: The author treats the linear second-order abstract Cauchy problem \[ \ddot u(t)+ B\dot u(t)+ Au(t)= 0,\quad u(0)= u_0,\;\dot u(0)= v_0 \] on a Hilbert space. Here \(A\) is selfadjoint and positive definite, \(B\) is \(m\)- accretive and invertible, and a compatibility condition for \(A\) and \(B\) is imposed. The problem is solved by rewriting the equation as a system \(\dot w(t)= {\mathcal A} w(t)\), with \[ {\mathcal A}:= \begin{pmatrix} 0 & Id\\ -A & - B\end{pmatrix}, \] and by treating this system on a scale of Hilbert spaces. In the appendix a new proof of a perturbation result for \(m\)-accretive operators is given.
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47D09
Mathematics Subject Classification ID: 47B44
zbMATH DE Number: 635925
zbMATH Keywords: linear second-order abstract Cauchy problem
zbMATH Keywords: scale of Hilbert spaces
zbMATH Keywords: perturbation result for \(m\)-accretive operators
author: Klaus-Jochen Engel
reviewed by: Jürgen Voigt
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1201
OpenAlex ID: W2036875912
DOI: 10.1006/JMAA.1994.1201
description: scientific article; zbMATH DE number 635925