EXISTENCE AND UNIQUENESS OF SOLUTION OF THE PROBLEM OF ACOUSTIC WAVE DIFFRACTION ON A SOLID HETEROGENEOUS BODY CONTAINING A SOFT SCREEN

Tsupak Aleksey Aleksandrovich, Candidate of physical and mathematical sciences, associate professor, sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), altsupak@yandex.ru

517.968, 517.983.37, 517.958:535.4

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 hetergene-ous body containing an infinitely thin acoustically soft screen.
Material and methods. The problem is considered in the quasiclassical formula-tion; 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, exis-tence, 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.

diffraction problem, quasiclassical solutions, integral equations, Sobolev spaces, pseudodifferential operators.

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