Presence and unicity of solution of the scalar problem of diffraction by a volumetric inhomogeneous solid with a piece-wise smooth refractive index

Background. The aim of the present paper is investigation of the direct scalar problem of plane wave scattering by a volumetric inhomogeneous solid, characterized by piece-wise smooth refractive index. Material and methods. The considered scattering problem is considered in the semiclassical formulation; the scattering problem is reduced to a weakly singular Fredholm integral equation of the second kind. Results. The semiclassical formulation of the scattering problem is proposed; the uniqueness theorem is proved for the scattering problem in differential formulation; the original problem is reduced to the Lippmann-Schwinger integral equation; equivalency between the integral equation of the second kind and the boundary value problem is proved. Conclusions. The obtained results on existence of a unique solution to the problem and its continuity obtained in the present article can be used for theoretical investigation of inverse problems of diffraction by compound volumetric obstacles.