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...
Main Authors: | , |
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Format: | Article |
Language: | English |
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Texas State University
2014-04-01
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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. |
first_indexed | 2024-12-23T19:49:14Z |
format | Article |
id | doaj.art-71716e97191a446686ba879c51a06e59 |
institution | Directory Open Access Journal |
issn | 1072-6691 |
language | English |
last_indexed | 2024-12-23T19:49:14Z |
publishDate | 2014-04-01 |
publisher | Texas State University |
record_format | Article |
series | Electronic Journal of Differential Equations |
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 |