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

Автор(и)

  • A.V. Khrabustovskyi Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering National Academy of Sciences of Ukraine 47 Lenin Ave., Kharkiv, 61103, Ukraine

Ключові слова:

Riemannian manifolds, wave equation, asymptotic behavior, homogenization.

Анотація

An asymptotic behavior of solution of the Cauchy problem for the wave equation is studied on the Riemannian manifold Me depending on a small parameter e. It is supposed that a topological type of Me increases as e → 0. The averaged equation is derived, it describes the asymptotic behavior of the original Cauchy problem as e → 0.

Mathematics Subject Classification: 35B27, 35K60.

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Як цитувати

(1)
Khrabustovskyi, A. Klein-Gordon Equation as a Result of Wave Equation Averaging on the Riemannian Manifold of Complex Microstructure. Журн. мат. фіз. анал. геом. 2007, 3, 213-233.

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