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

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.