Existence and uniqueness of solution of the problem of acoustic wave diffraction on a solid heterogeneous body containing a soft screen

Background. The aim of this work is to theoretically study the scalar problem of plane wave scattering by an obstacle of a complex shape; the obstacle is a hetergeneous body containing an infinitely thin acoustically soft screen. Material and methods. The problem is considered in the quasiclassical formulation; the original boundary value problem is reduced to a system of weakly singular integral equations; the properties of the system are studied using pseudodifferential operators on manifolds with boundary. Results. The author has proposed a quasiclassical formulation of the diffraction problem; proved the theorem on uniqueness of the quasi-classical solution to the boundary value problem; the boundary value problem has been reduced to a system of integral equations; equivalence of two statements of the problem has been proved, as well as invertibility of the matrix integral operator. Conclusions. The researcher has obtained important results on uniqueness, existence, and continuity of the quasiclassical solution to the diffraction problem; these results can be used for validation of numerical methods for approximate solving of the diffraction problem.