Averaging and control of wave propagation in rapidly varying media

An averaging approach to solving hyperbolic partial differential equations with rapidly oscillating characteristic curves is presented. These equations describe a general case of wave propagation through rapidly varying media, where the variations are periodic with high frequency and could be spatial as well as temporal. In addition, we solve the problem of controlling rapidly oscillating characteristic curves of the system. In an averaged sense, we lay a basis for controlling the corresponding medium and wave propagation through that medium