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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| Дата: | 2012 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2012
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106726 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
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irk-123456789-1067262016-10-04T03:02:17Z On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis Khalina, K.S. 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. 2012 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/106726 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Khalina, K.S. |
| spellingShingle |
Khalina, K.S. On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis Журнал математической физики, анализа, геометрии |
| author_facet |
Khalina, K.S. |
| author_sort |
Khalina, K.S. |
| title |
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_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_sort |
on the neumann boundary controllability for the non-homogeneous string on a half-axis |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106726 |
| 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. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
AT khalinaks ontheneumannboundarycontrollabilityforthenonhomogeneousstringonahalfaxis |
| first_indexed |
2023-10-18T20:13:34Z |
| last_indexed |
2023-10-18T20:13:34Z |
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1796149302873030656 |