Exact controllability for a wave equation with mixed boundary conditions in a non-cylindrical domain

In this article we study the exact controllability of a one-dimensional wave equation with mixed boundary conditions in a non-cylindrical domain. The fixed endpoint has a Dirichlet-type boundary condition, while the moving end has a Neumann-type condition. When the speed of the moving endpoint...

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Main Authors: Lizhi Cui, Hang Gao
Format: Article
Language:English
Published: Texas State University 2014-04-01
Series:Electronic Journal of Differential Equations
Subjects:
Online Access:http://ejde.math.txstate.edu/Volumes/2014/101/abstr.html
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author Lizhi Cui
Hang Gao
author_facet Lizhi Cui
Hang Gao
author_sort Lizhi Cui
collection DOAJ
description In this article we study the exact controllability of a one-dimensional wave equation with mixed boundary conditions in a non-cylindrical domain. The fixed endpoint has a Dirichlet-type boundary condition, while the moving end has a Neumann-type condition. When the speed of the moving endpoint is less than the characteristic speed, the exact controllability of this equation is established by Hilbert Uniqueness Method. Moreover, we shall give the explicit dependence of the controllability time on the speed of the moving endpoint.
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spelling doaj.art-71716e97191a446686ba879c51a06e592022-12-21T17:33:25ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912014-04-012014101,112Exact controllability for a wave equation with mixed boundary conditions in a non-cylindrical domainLizhi Cui0Hang Gao1 Jilin Univ. of Finance and Economics, Changchun, China Northeast Normal Univ., Changchun, China In this article we study the exact controllability of a one-dimensional wave equation with mixed boundary conditions in a non-cylindrical domain. The fixed endpoint has a Dirichlet-type boundary condition, while the moving end has a Neumann-type condition. When the speed of the moving endpoint is less than the characteristic speed, the exact controllability of this equation is established by Hilbert Uniqueness Method. Moreover, we shall give the explicit dependence of the controllability time on the speed of the moving endpoint.http://ejde.math.txstate.edu/Volumes/2014/101/abstr.htmlExact controllabilitywave equationmixed boundary conditionsnon-cylindrical domain
spellingShingle Lizhi Cui
Hang Gao
Exact controllability for a wave equation with mixed boundary conditions in a non-cylindrical domain
Electronic Journal of Differential Equations
Exact controllability
wave equation
mixed boundary conditions
non-cylindrical domain
title Exact controllability for a wave equation with mixed boundary conditions in a non-cylindrical domain
title_full Exact controllability for a wave equation with mixed boundary conditions in a non-cylindrical domain
title_fullStr Exact controllability for a wave equation with mixed boundary conditions in a non-cylindrical domain
title_full_unstemmed Exact controllability for a wave equation with mixed boundary conditions in a non-cylindrical domain
title_short Exact controllability for a wave equation with mixed boundary conditions in a non-cylindrical domain
title_sort exact controllability for a wave equation with mixed boundary conditions in a non cylindrical domain
topic Exact controllability
wave equation
mixed boundary conditions
non-cylindrical domain
url http://ejde.math.txstate.edu/Volumes/2014/101/abstr.html
work_keys_str_mv AT lizhicui exactcontrollabilityforawaveequationwithmixedboundaryconditionsinanoncylindricaldomain
AT hanggao exactcontrollabilityforawaveequationwithmixedboundaryconditionsinanoncylindricaldomain