Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction
In the paper, the spectral problem generated by the Sturm-Liouville equation -y'' + q(x)y = (λ² - ip(x)λ)y, where q(x) is a real L₂(0, a)-function and p(x) is a peace-wise constant, is considered with the Dirichlet boundary conditions at the ends of the interval (0, a). The spectrum of the...
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| Дата: | 2012 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2012
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106724 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction / L. Kobyakova // Журнал математической физики, анализа, геометрии. — 2012. — Т. 8, № 3. — С. 280-295. — Бібліогр.: 19 назв. — англ. |
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dspace |
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irk-123456789-1067242016-10-04T03:02:32Z Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction Kobyakova, L. In the paper, the spectral problem generated by the Sturm-Liouville equation -y'' + q(x)y = (λ² - ip(x)λ)y, where q(x) is a real L₂(0, a)-function and p(x) is a peace-wise constant, is considered with the Dirichlet boundary conditions at the ends of the interval (0, a). The spectrum of the problem is compared with the spectra of auxiliary problems with the Dirichlet-Dirichlet and the Dirichlet-Neumann boundary conditions on the halves of the interval. Asymptotic formulas are obtained for the eigenvalues of this problem. В статье рассматривается спектральная задача, порожденная уравнением Штурма-Лиувилля -y'' + q(x)y = (λ² - ip(x)λ)y, где q(x) - вещественная L₂(0, a)-функция, а p(x) является кусочно-постоянной, с краевыми условиями Дирихле на концах интервала (0, a). Спектр данной задачи сравнивается со спектром вспомогательной задачи с краевыми условиями Дирихле-Дирихле и Дирихле-Неймана на полуинтервалах. Получены асимптотические формулы для собственных значений задачи. 2012 Article Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction / L. Kobyakova // Журнал математической физики, анализа, геометрии. — 2012. — Т. 8, № 3. — С. 280-295. — Бібліогр.: 19 назв. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106724 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 spectral problem generated by the Sturm-Liouville equation -y'' + q(x)y = (λ² - ip(x)λ)y, where q(x) is a real L₂(0, a)-function and p(x) is a peace-wise constant, is considered with the Dirichlet boundary conditions at the ends of the interval (0, a). The spectrum of the problem is compared with the spectra of auxiliary problems with the Dirichlet-Dirichlet and the Dirichlet-Neumann boundary conditions on the halves of the interval. Asymptotic formulas are obtained for the eigenvalues of this problem. |
| format |
Article |
| author |
Kobyakova, L. |
| spellingShingle |
Kobyakova, L. Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction Журнал математической физики, анализа, геометрии |
| author_facet |
Kobyakova, L. |
| author_sort |
Kobyakova, L. |
| title |
Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction |
| title_short |
Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction |
| title_full |
Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction |
| title_fullStr |
Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction |
| title_full_unstemmed |
Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction |
| title_sort |
spectral problem generated by the equation of smooth string with piece-wise constant friction |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106724 |
| citation_txt |
Spectral Problem Generated by the Equation of Smooth String with Piece-Wise Constant Friction / L. Kobyakova // Журнал математической физики, анализа, геометрии. — 2012. — Т. 8, № 3. — С. 280-295. — Бібліогр.: 19 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
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AT kobyakoval spectralproblemgeneratedbytheequationofsmoothstringwithpiecewiseconstantfriction |
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2023-10-18T20:13:33Z |
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2023-10-18T20:13:33Z |
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1796149302663315456 |