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: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/827698 |
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| _version_ | 1850167495685570560 |
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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. |
| format | Article |
| id | doaj-art-d984393cec384f13948c0a60fd4e190c |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| 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 |