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On the Fredholm Property and Solvability of a System of Integral Equations in the Transmission Problem for the Helmholtz Equation

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Abstract

A scalar three-dimensional boundary value problem of wave diffraction for the Helmholtz equation with transmission conditions that assume the presence of an infinitely thin material at the media interface is considered. Uniqueness and existence theorems for solutions are proved. The original problem is reduced to a system of integral equations over the media interface. Calculation formulas for the system of linear algebraic equations obtained after applying the collocation method and numerical results for solving the problem when the domain is a ball with certain transmission conditions are given.

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Funding

This work was financially supported by the Russian Science Foundation, project 20-11-20087, https://rscf.ru/en/project/20-11-20087/.

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Authors and Affiliations

  1. Penza State University, Penza, 440026, Russia

    Yu. G. Smirnov & O. V. Kondyrev

Authors
  1. Yu. G. Smirnov
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  2. O. V. Kondyrev
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Correspondence to Yu. G. Smirnov or O. V. Kondyrev.

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Translated by V. Potapchouck

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Smirnov, Y.G., Kondyrev, O.V. On the Fredholm Property and Solvability of a System of Integral Equations in the Transmission Problem for the Helmholtz Equation. Diff Equat 59, 1095–1104 (2023). https://doi.org/10.1134/S0012266123080086

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  • DOI: https://doi.org/10.1134/S0012266123080086

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