A generation result for cosine functions of operators
type: Item
instance of: scholarly article
title: A generation result for cosine functions of operators
zbMATH Open document ID: 1195.47030
DOI: 10.4171/ZAA/1375
author: Hernán R. Henríquez
author: Carlos Landero H.
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2009-01-30T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: In this paper, the authors investigate the generation problem of cosine functions of linear operators. Suppose that \(A\) is closed and densely defined linear operator on a Banach space \(X\). Then the authors prove that for the abstract second order Cauchy problem, the equation has a unique weak solution for each pair \( x_0, x_1\in X \) if and only if \(A\) generates a strongly continuous cosine function of linear operators. As an application, they discuss the self-accessibility of the abstract second order system.
Mathematics Subject Classification ID: 47D09
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 5500726
zbMATH Keywords: cosine functions of operators
zbMATH Keywords: infinitesimal generator
zbMATH Keywords: control system of second order
reviewed by: Gen Qi Xu
MaRDI profile type: Publication
cites work: Q2716079
cites work: Shorter Notes: Strongly Continuous Semigroups, Weak Solutions, and the Variation of Constants Formula
cites work: An abstract nonlinear second order differential equation
cites work: Q3678037
cites work: Q5632400
cites work: Q5526484
cites work: The functional calculus for sectorial operators
cites work: On non-exact controllable systems
cites work: A geometric property of control systems with states in a Banach space
cites work: Differentiability of solutions of the second order abstract Cauchy problem
cites work: Mathematical Systems Theory I
cites work: On cosine operator functions and one-parameter groups of operators
cites work: Periodische operatorwertige Cosinusfunktionen
cites work: Approximate controllability for a class of abstract second-order functional evolution equations
cites work: Controllability of second-order neutral functional differential inclusions in Banach spaces
cites work: Q4167185
cites work: Cosine families and abstract nonlinear second order differential equations
cites work: Q3903316
cites work: Q4156649
cites work: On the Relationship between First and Second Order Controllable Systems in Banach Spaces
cites work: Remarks on Controllability of Second Order Evolution Equations in Hilbert Spaces
description: scientific article; zbMATH DE number 5500726