On the Neumann Boundary Controllability for the Non-Homogeneous String on a Segment
The control system wtt = wxx - q(x)w, wx(0; t) = u(t), wx(d, t) = 0, x is in (0; d), t is in (0; T), d > 0, 0 < T ≤ d is considered. Here q is in C¹[0, d], q > 0, q'₊(0) = q₋(d) = 0, u is a control, |u(t)| ≤ 1 on (0, T). The necessary and suffcient conditions of null-controllability an...
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| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2011
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106688 |
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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 Segment / K.S. Khalina // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 4. — С. 333-351. — Бібліогр.: 23 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-106688 |
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dspace |
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irk-123456789-1066882016-10-03T03:02:20Z On the Neumann Boundary Controllability for the Non-Homogeneous String on a Segment Khalina, K.S. The control system wtt = wxx - q(x)w, wx(0; t) = u(t), wx(d, t) = 0, x is in (0; d), t is in (0; T), d > 0, 0 < T ≤ d is considered. Here q is in C¹[0, d], q > 0, q'₊(0) = q₋(d) = 0, u is a control, |u(t)| ≤ 1 on (0, T). The necessary and suffcient conditions of null-controllability and approximate null-controllability are obtained for this system. The controllability problems are considered in the modified Sobolev spaces. The controls that solve these problems are found explicitly. It is proved that among the solutions of the Markov trigonometric moment problem there are bang-bang controls solving the approximate null-controllability problem. 2011 Article On the Neumann Boundary Controllability for the Non-Homogeneous String on a Segment / K.S. Khalina // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 4. — С. 333-351. — Бібліогр.: 23 назв. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106688 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 |
The control system wtt = wxx - q(x)w, wx(0; t) = u(t), wx(d, t) = 0, x is in (0; d), t is in (0; T), d > 0, 0 < T ≤ d is considered. Here q is in C¹[0, d], q > 0, q'₊(0) = q₋(d) = 0, u is a control, |u(t)| ≤ 1 on (0, T). The necessary and suffcient conditions of null-controllability and approximate null-controllability are obtained for this system. The controllability problems are considered in the modified Sobolev spaces. The controls that solve these problems are found explicitly. It is proved that among the solutions of the Markov trigonometric moment problem there are bang-bang controls solving the approximate null-controllability problem. |
| format |
Article |
| author |
Khalina, K.S. |
| spellingShingle |
Khalina, K.S. On the Neumann Boundary Controllability for the Non-Homogeneous String on a Segment 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 Segment |
| title_short |
On the Neumann Boundary Controllability for the Non-Homogeneous String on a Segment |
| title_full |
On the Neumann Boundary Controllability for the Non-Homogeneous String on a Segment |
| title_fullStr |
On the Neumann Boundary Controllability for the Non-Homogeneous String on a Segment |
| title_full_unstemmed |
On the Neumann Boundary Controllability for the Non-Homogeneous String on a Segment |
| title_sort |
on the neumann boundary controllability for the non-homogeneous string on a segment |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106688 |
| citation_txt |
On the Neumann Boundary Controllability for the Non-Homogeneous String on a Segment / K.S. Khalina // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 4. — С. 333-351. — Бібліогр.: 23 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
AT khalinaks ontheneumannboundarycontrollabilityforthenonhomogeneousstringonasegment |
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2023-10-18T20:13:29Z |
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2023-10-18T20:13:29Z |
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1796149299925483520 |