Klein-Gordon Equation as a Result of Wave Equation Averaging on the Riemannian Manifold of Complex Microstructure
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 $M^\varepsilon$ depending on a small parameter $\varepsilon$. It is supposed that a topological type of $M^\varepsilon$ increases as $\varepsilon\to 0$. The averaged equation is derived, it describes the asymptotic behavior of the original Cauchy problem as $\varepsilon\to 0$.
Mathematics Subject Classification: 35B27, 35K60.
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Khrabustovskyi, A. V. 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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