On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis
In the paper, the equation of a vibrating non-homogeneous string, whose potential is not equal to a constant, is considered on a half-axis. The Neumann control of the class L∞ is considered at a point x = 0. The control problem is studied in the Sobolev spaces. The suffcient conditions for nullcontr...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2012 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106726 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis / K.S. Khalina // Журнал математической физики, анализа, геометрии. — 2012. — Т. 8, № 4. — С. 307-335. — Бібліогр.: 26 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862744141367083008 |
|---|---|
| author | Khalina, K.S. |
| author_facet | Khalina, K.S. |
| citation_txt | On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis / K.S. Khalina // Журнал математической физики, анализа, геометрии. — 2012. — Т. 8, № 4. — С. 307-335. — Бібліогр.: 26 назв. — англ. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | In the paper, the equation of a vibrating non-homogeneous string, whose potential is not equal to a constant, is considered on a half-axis. The Neumann control of the class L∞ is considered at a point x = 0. The control problem is studied in the Sobolev spaces. The suffcient conditions for nullcontrollability and approximate null-controllability at a free time T > 0 are obtained for the given system. The controls solving these problems are found explicitly.
Рассмотрено уравнение колебания неоднородной струны на полуоси с потенциалом, не равным константе. На левом конце рассмотрено управление типа Неймана из класса L∞. Задача управляемости изучена в пространствах Соболева. Для заданной системы получены достаточные условия 0-управляемости и ε-управляемости за свободное время T > 0. Управления, которые решают эти задачи, найдены в явном виде.
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| first_indexed | 2025-12-07T20:34:09Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-106726 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T20:34:09Z |
| publishDate | 2012 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Khalina, K.S. 2016-10-03T16:46:00Z 2016-10-03T16:46:00Z 2012 On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis / K.S. Khalina // Журнал математической физики, анализа, геометрии. — 2012. — Т. 8, № 4. — С. 307-335. — Бібліогр.: 26 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106726 In the paper, the equation of a vibrating non-homogeneous string, whose potential is not equal to a constant, is considered on a half-axis. The Neumann control of the class L∞ is considered at a point x = 0. The control problem is studied in the Sobolev spaces. The suffcient conditions for nullcontrollability and approximate null-controllability at a free time T > 0 are obtained for the given system. The controls solving these problems are found explicitly. Рассмотрено уравнение колебания неоднородной струны на полуоси с потенциалом, не равным константе. На левом конце рассмотрено управление типа Неймана из класса L∞. Задача управляемости изучена в пространствах Соболева. Для заданной системы получены достаточные условия 0-управляемости и ε-управляемости за свободное время T > 0. Управления, которые решают эти задачи, найдены в явном виде. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis Article published earlier |
| spellingShingle | On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis Khalina, K.S. |
| title | On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis |
| title_full | On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis |
| title_fullStr | On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis |
| title_full_unstemmed | On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis |
| title_short | On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis |
| title_sort | on the neumann boundary controllability for the non-homogeneous string on a half-axis |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106726 |
| work_keys_str_mv | AT khalinaks ontheneumannboundarycontrollabilityforthenonhomogeneousstringonahalfaxis |