Controllability for a Wave Equation with Moving Boundary

We investigate the controllability for a one-dimensional wave equation in domains with moving boundary. This model characterizes small vibrations of a stretched elastic string when one of the two endpoints varies. When the speed of the moving endpoint is less than 1-1/e, by Hilbert uniqueness method...

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Main Authors: Lizhi Cui, Libo Song
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/827698
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author Lizhi Cui
Libo Song
author_facet Lizhi Cui
Libo Song
author_sort Lizhi Cui
collection DOAJ
description We investigate the controllability for a one-dimensional wave equation in domains with moving boundary. This model characterizes small vibrations of a stretched elastic string when one of the two endpoints varies. When the speed of the moving endpoint is less than 1-1/e, by Hilbert uniqueness method, sidewise energy estimates method, and multiplier method, we get partial Dirichlet boundary controllability. Moreover, we will give a sharper estimate on controllability time that only depends on the speed of the moving endpoint.
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issn 1110-757X
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language English
publishDate 2014-01-01
publisher Wiley
record_format Article
series Journal of Applied Mathematics
spelling doaj-art-d984393cec384f13948c0a60fd4e190c2025-08-20T02:21:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/827698827698Controllability for a Wave Equation with Moving BoundaryLizhi Cui0Libo Song1College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, ChinaEducational Administration, Jilin University of Finance and Economics, Changchun 130117, ChinaWe investigate the controllability for a one-dimensional wave equation in domains with moving boundary. This model characterizes small vibrations of a stretched elastic string when one of the two endpoints varies. When the speed of the moving endpoint is less than 1-1/e, by Hilbert uniqueness method, sidewise energy estimates method, and multiplier method, we get partial Dirichlet boundary controllability. Moreover, we will give a sharper estimate on controllability time that only depends on the speed of the moving endpoint.http://dx.doi.org/10.1155/2014/827698
spellingShingle Lizhi Cui
Libo Song
Controllability for a Wave Equation with Moving Boundary
Journal of Applied Mathematics
title Controllability for a Wave Equation with Moving Boundary
title_full Controllability for a Wave Equation with Moving Boundary
title_fullStr Controllability for a Wave Equation with Moving Boundary
title_full_unstemmed Controllability for a Wave Equation with Moving Boundary
title_short Controllability for a Wave Equation with Moving Boundary
title_sort controllability for a wave equation with moving boundary
url http://dx.doi.org/10.1155/2014/827698
work_keys_str_mv AT lizhicui controllabilityforawaveequationwithmovingboundary
AT libosong controllabilityforawaveequationwithmovingboundary