Homogenization of hyperbolic equations (Q524120)

In this paper the authors deal with a problem of homogenization concerning the hyperbolic equations with rapidly oscillating coefficients. A second order self-adjoint elliptic operator acting on \(L^2\) is presented in a factorized form, where a factor is a Hermitian matrix-valued function which is periodic with respect to a lattice \(\Gamma\), bounded, and uniformly positive definite. It is also considered a more general operator with another matrix valued factor bounded with his inverse. Estimates are obtained in the norm of operator cosine and an effective operator with constant coefficients is obtained and sharp order estimates are achieved. Applications are related to the acoustic problems and to elasticity theory.