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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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2011 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
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| Summary: | 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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| ISSN: | 1812-9471 |