Klein-Gordon Equation as a Result of Wave Equation Averaging on the Riemannian Manifold of Complex Microstructure
An asymptotic behavior of solution of the Cauchy problem for the wave equation is studied on the Riemannian manifold Mε depending on a small parameter ε. It is supposed that a topological type of Mε increases as ε → 0. The averaged equation is derived, it describes the asymptotic behavior of the ori...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2007 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106446 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Klein-Gordon Equation as a Result of Wave Equation Averaging on the Riemannian Manifold of Complex Microstructure / A.V. Khrabustovskyi // Журнал математической физики, анализа, геометрии. — 2007. — Т. 3, № 2. — С. 213-233. — Бібліогр.: 5 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | An asymptotic behavior of solution of the Cauchy problem for the wave equation is studied on the Riemannian manifold Mε depending on a small parameter ε. It is supposed that a topological type of Mε increases as ε → 0. The averaged equation is derived, it describes the asymptotic behavior of the original Cauchy problem as ε → 0.
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| ISSN: | 1812-9471 |