Klein-Gordon Equation as a Result of Wave Equation Averaging on the Riemannian Manifold of Complex Microstructure - Khrabustovskyi, A.V. (Журнал математической физики, анализа, геометрии, 2007)
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 original Cauchy problem as ε → 0.