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Abstract <p> The paper focuses on a boundary value problem for a system of two homogeneousHelmholtz equations with mixed boundary conditions arising in the theory of electromagneticwave scattering on structures covered with two-dimensional materials. The problem is reduced toa boundary integral equation on the entire real line involving a hypersingular integral operator.Introducing new variables and unknown function, one passes to an integral equation onan interval. To find an approximate solution of the resulting equation, a collocation method usingFourier–Chebyshev series to represent the solution is suggested; hypersingular integrals arecalculated analytically. In the main part of the paper, we prove the Fredholm property of thehypersingular operator involved in the integral equation under consideration.</p>

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On the Fredholm Property of a Hypersingular Integral Operator in a Problem of Electromagnetic Wave Scattering on a Slab Covered with Graphene

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Yu. G. Smirnov,
  • S. V. Tikhov

摘要

Abstract

The paper focuses on a boundary value problem for a system of two homogeneousHelmholtz equations with mixed boundary conditions arising in the theory of electromagneticwave scattering on structures covered with two-dimensional materials. The problem is reduced toa boundary integral equation on the entire real line involving a hypersingular integral operator.Introducing new variables and unknown function, one passes to an integral equation onan interval. To find an approximate solution of the resulting equation, a collocation method usingFourier–Chebyshev series to represent the solution is suggested; hypersingular integrals arecalculated analytically. In the main part of the paper, we prove the Fredholm property of thehypersingular operator involved in the integral equation under consideration.