On convergence to equilibrium distribution for wave equation in even dimensions
Alexander Komech, Elena Andreevna Kopylova, Norbert J. Mauser · Ergodic Theory and Dynamical Systems · 2004
Consider a wave equation (WE) with constant coefficients in which gives a Central Limit Theorem (CLT) for the WE. The proof for the case of constant coefficients is based on stationary phase asymptotics of the solution in the Fourier representation and Bernstein's ‘room–corridor’ argument. The case of variable coefficients is reduced to that of constant ones by a version of the scattering theory, based on Vainberg's results on local energy decay.