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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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/140546 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862691410708267008 |
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| author | Fardigola, L.V. |
| author_facet | Fardigola, L.V. |
| 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| 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.
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| first_indexed | 2025-12-07T16:15:50Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-140546 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T16:15:50Z |
| publishDate | 2016 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Fardigola, L.V. 2018-07-10T10:49:37Z 2018-07-10T10:49:37Z 2016 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. https://nasplib.isofts.kiev.ua/handle/123456789/140546 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. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis Article published earlier |
| spellingShingle | Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis Fardigola, L.V. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/140546 |
| work_keys_str_mv | AT fardigolalv transformationoperatorsandmodifiedsobolevspacesincontrollabilityproblemsonahalfaxis |