Time harmonic acoustic scattering in anisotropic media

The scattering problem of a plane or a point source generated wave is considered for the case where both the medium of propagation and the interior of the scatterer exhibit their own anisotropies. A particular redirected gradient operator is introduced, which carries all directional characteristics of the anisotropic medium. Once the fundamental solution is obtained, integral representations for the scattered as well as for the interior and the total fields are generated. For such media even the handling of the singularities, in generating integral representations, depends on the characteristics of the particular medium. A modified, also medium dependent, radiation condition is introduced. Detailed asymptotic analysis leads to an integral representation for the scattering amplitude. The associated energy functionals are presented and the relative cross sections are also defined. Copyright (c) 2005 John Wiley & Sons, Ltd.