On uniqueness of solution of the problem of acoustic wave diffraction on a system of non-intersecting screens and heterogeneous bodies

Background. The work is aimed at theoretical study of the scalar problem of plane wave scattering by an obstacle of complex shape consisting of several solid bodies, infinitely thin, acoustically soft and acoustically hard screens. Materials and methods. The problem is considered in the quasiclassical formulation (solution is sought in the classical sense everywhere except the screen boundary); to prove the main theorem the author used classical integral formulas generalized for the elements of Soboblev spaces as well as the trace theory for pseudodifferential operators on manifolds with a boundary. Results. The researcher suggests the quasiclassical formulation of the diffraction problem; the theorem on uniqueness of the quasi-classical solution of the boundary value problem was proved. Conclusions. The suggested research method allows to obtain the important result on the uniqueness of the quasi-classical solution of the diffraction problem and can be used in the study of solvability of integral equations which arise in the diffraction theory as well as for validation of numerical methods of approximate solution thereof.