Klein-Gordon Equation as a Result of Wave Equation Averaging on the Riemannian Manifold of Complex Microstructure - Khrabustovskyi, A. V. (Журнал математичної фізики, аналізу, геометрії, 2007)
An asymptotic behavior of solution of the Cauchy problem for the wave equation is studied on the Riemannian manifold $M^ε$ depending on a small parameter $ε$. It is supposed that a topological type of $M^ε$ increases as $ε→ 0$. The averaged equation is derived, it describes the asymptotic behavior of the original Cauchy problem as $ε→ 0$. Mathematics Subject Classification: 35B27, 35K60.