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-controllabilit...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2011 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106688 |
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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 Segment / K.S. Khalina // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 4. — С. 333-351. — Бібліогр.: 23 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862709828662591488 |
|---|---|
| author | Khalina, K.S. |
| author_facet | Khalina, K.S. |
| 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| 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.
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| first_indexed | 2025-12-07T17:20:43Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106688 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T17:20:43Z |
| publishDate | 2011 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Khalina, K.S. 2016-10-02T20:17:26Z 2016-10-02T20:17:26Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/106688 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. 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 Segment Article published earlier |
| spellingShingle | On the Neumann Boundary Controllability for the Non-Homogeneous String on a Segment Khalina, K.S. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106688 |
| work_keys_str_mv | AT khalinaks ontheneumannboundarycontrollabilityforthenonhomogeneousstringonasegment |