Klein-Gordon Equation as a Result of Wave Equation Averaging on the Riemannian Manifold of Complex Microstructure

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2007
• Main Author: Khrabustovskyi, A.V.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/106446
• 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.

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...