Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time
We study the Cauchy problem for the inhomogeneous two-dimensional wave equation with variable coefficients and zero initial data. The righthand side is assumed to be localized in space and time. The equation is considered in a domain with a boundary (shore). The velocity is assumed to vanish on the...
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| Дата: | 2018 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2018
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/145880 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time / A. Anikin, S. Dobrokhotov, V. Nazaikinskii // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 4. — С. 393-405. — Бібліогр.: 30 назв. — англ. |
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irk-123456789-1458802019-02-03T01:23:19Z Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time Anikin, A. Dobrokhotov, S. Nazaikinskii, V. We study the Cauchy problem for the inhomogeneous two-dimensional wave equation with variable coefficients and zero initial data. The righthand side is assumed to be localized in space and time. The equation is considered in a domain with a boundary (shore). The velocity is assumed to vanish on the shore as a square root of the distance to the shore, that is, the wave equation has a singularity on the curve. This curve determines the boundary of the domain where the problem is studied. The main result of the paper is efficient asymptotic formulas for the solution of this problem, including the neighborhood of the shore. Вивчається задача Кошi для неоднорiдного двовимiрного хвильового рiвняння зi змiнними коефiцiєнтами та нульовими початковими даними. Вважається, що права частина локалiзована в просторi та часi. Рiвняння розглядається в областi з межею (берегом). Вважається, що швидкiсть на березi зникає як квадратний корiнь вiдстанi до берега, тобто хвильове рiвняння має задану на кривiй особливiсть. Ця крива i визначає межу областi, в якiй вивчається задача. Основний результат роботи - ефективнi асимптотичнi формули для розв’язку зазначеноЁ задачi, включаючи окiл берега. 2018 Article Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time / A. Anikin, S. Dobrokhotov, V. Nazaikinskii // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 4. — С. 393-405. — Бібліогр.: 30 назв. — англ. 1812-9471 DOI: https://doi.org/10.15407/mag14.04.393 Mathematics Subject Classification 2000: 34E20, 35L05, 35Q35 http://dspace.nbuv.gov.ua/handle/123456789/145880 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 |
We study the Cauchy problem for the inhomogeneous two-dimensional wave equation with variable coefficients and zero initial data. The righthand side is assumed to be localized in space and time. The equation is considered in a domain with a boundary (shore). The velocity is assumed to vanish on the shore as a square root of the distance to the shore, that is, the wave equation has a singularity on the curve. This curve determines the boundary of the domain where the problem is studied. The main result of the paper is efficient asymptotic formulas for the solution of this problem, including the neighborhood of the shore. |
| format |
Article |
| author |
Anikin, A. Dobrokhotov, S. Nazaikinskii, V. |
| spellingShingle |
Anikin, A. Dobrokhotov, S. Nazaikinskii, V. Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time Журнал математической физики, анализа, геометрии |
| author_facet |
Anikin, A. Dobrokhotov, S. Nazaikinskii, V. |
| author_sort |
Anikin, A. |
| title |
Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time |
| title_short |
Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time |
| title_full |
Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time |
| title_fullStr |
Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time |
| title_full_unstemmed |
Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time |
| title_sort |
asymptotic solutions of the wave equation with degenerate velocity and with right-hand side localized in space and time |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2018 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/145880 |
| citation_txt |
Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time / A. Anikin, S. Dobrokhotov, V. Nazaikinskii // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 4. — С. 393-405. — Бібліогр.: 30 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
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2023-05-20T17:23:18Z |
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2023-05-20T17:23:18Z |
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1796153181594451968 |