Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis
In the paper, the control system wₜₜ =1/ρ(kwₓ)ₓ + γw, wₓ(0, t) = u(t), x > 0, t belongs (0, T), is considered in special modified spaces of Sobolev type Here ρ, k, and γ are given functions on [0, +∞); u belongs L∞(0, ∞) is a control; T > 0 is a constant. The growth of distributions from thes...
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| Дата: | 2016 |
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| Формат: | Стаття |
| Мова: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2016
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/140546 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis / L.V. Fardigola // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 1. — С. 17-47. — Бібліогр.: 40 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1405462018-07-11T01:23:03Z Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis Fardigola, L.V. In the paper, the control system wₜₜ =1/ρ(kwₓ)ₓ + γw, wₓ(0, t) = u(t), x > 0, t belongs (0, T), is considered in special modified spaces of Sobolev type Here ρ, k, and γ are given functions on [0, +∞); u belongs L∞(0, ∞) is a control; T > 0 is a constant. The growth of distributions from these spaces depends on the growth of ρ and k. With the aid of some transformation operators, it is proved that the control system replicates the controllability properties of the auxiliary system zₜₜ = zξξ − q²z, zξ(0, t) = v(t), ξ > 0, t belongs (0, T), and vise versa. Here q ≥ 0 is a constant and v belongs L∞(0, ∞) is a control. For the main system, necessary and sufficient conditions of the L∞-controllability and the approximate L∞-controllability are obtained from those known for the auxiliary system. 2016 Article Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis / L.V. Fardigola // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 1. — С. 17-47. — Бібліогр.: 40 назв. — англ. 1812-9471 DOI: doi.org/10.15407/mag12.01.017 Mathematics Subject Classification 2000: 93B05, 35B30, 35L05. http://dspace.nbuv.gov.ua/handle/123456789/140546 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 control system wₜₜ =1/ρ(kwₓ)ₓ + γw, wₓ(0, t) = u(t), x > 0, t belongs (0, T), is considered in special modified spaces of Sobolev type Here ρ, k, and γ are given functions on [0, +∞); u belongs L∞(0, ∞) is a control; T > 0 is a constant. The growth of distributions from these spaces depends on the growth of ρ and k. With the aid of some transformation operators, it is proved that the control system replicates the controllability properties of the auxiliary system zₜₜ = zξξ − q²z, zξ(0, t) = v(t), ξ > 0, t belongs (0, T), and vise versa. Here q ≥ 0 is a constant and v belongs L∞(0, ∞) is a control. For the main system, necessary and sufficient conditions of the L∞-controllability and the approximate L∞-controllability are obtained from those known for the auxiliary system. |
| format |
Article |
| author |
Fardigola, L.V. |
| spellingShingle |
Fardigola, L.V. Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis Журнал математической физики, анализа, геометрии |
| author_facet |
Fardigola, L.V. |
| author_sort |
Fardigola, L.V. |
| title |
Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis |
| title_short |
Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis |
| title_full |
Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis |
| title_fullStr |
Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis |
| title_full_unstemmed |
Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis |
| title_sort |
transformation operators and modified sobolev spaces in controllability problems on a half-axis |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/140546 |
| citation_txt |
Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis / L.V. Fardigola // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 1. — С. 17-47. — Бібліогр.: 40 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
AT fardigolalv transformationoperatorsandmodifiedsobolevspacesincontrollabilityproblemsonahalfaxis |
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2023-10-18T21:22:53Z |
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2023-10-18T21:22:53Z |
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1796152661004779520 |