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Method of integral equations in the scalar problem of diffraction on a system consisting of a “soft” and a “hard” screen and an inhomogeneous body

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Abstract

We consider the scalar problem on the diffraction of a plane wave on a system of two screens with boundary conditions of the first and the second kind and a solid inhomogeneous body in the semiclassical setting. The original boundary value problem for the Helmholtz equation is reduced to a system of singular integral equations over the body domain and the screen surfaces. We prove the equivalence of the integral and differential statements of the problem, the solvability of the system of integral equations in Sobolev spaces, and the smoothness of its solutions. To solve the integral equations approximately, we use the Bubnov-Galerkin method; we introduce basis functions on the body and the screens and prove the consistency and convergence of the numerical method.

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Authors and Affiliations

  1. Penza State University, Penza, Russia

    Yu. G. Smirnov & A. A. Tsupak

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  1. Yu. G. Smirnov
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  2. A. A. Tsupak
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Correspondence to Yu. G. Smirnov.

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Original Russian Text © Yu.G. Smirnov, A.A. Tsupak, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 9, pp. 1164–1174.

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Smirnov, Y.G., Tsupak, A.A. Method of integral equations in the scalar problem of diffraction on a system consisting of a “soft” and a “hard” screen and an inhomogeneous body. Diff Equat 50, 1150–1160 (2014). https://doi.org/10.1134/S0012266114090031

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  • DOI: https://doi.org/10.1134/S0012266114090031

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