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.