An acoustic scattering problem for periodic,inhomogeneous media

We study the problem of the scattering by a periodic, inhomogeneous, penetrable medium. Using the Dirichlet-to-Neumann operator from the classical formulation of the problem we derive a variational equation and give regularity result to show the equivalence of both formulations. We present certain uniqueness results, which by the Fredholm alternative yield existence of the solution and its continuous dependence on the incoming wave. We prove existence of a solution for special incident waves even if there is no uniqueness. A result about analytical dependence of the solution on the wave number and the incident angle is given. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.