Non-linear wave propagation in a layered half space

In this paper we consider the one dimensional propagation of weak discontinuities through a layered half space where quasilinear hyperbolic systems in homogeneous conservative form are involved. The amplitude of reflected and transmitted discontinuities across each layer is determined in terms of the initial conditions. The critical time when the incident wave breaks down is discussed. The results are specialized in the case of periodic layering. Physical examples are considered at the end of the paper.