ON THE FREDHOLM PROPERTY OF A HYPERSINGULAR INTEGRAL OPERATOR IN A SCATTERING PROBLEM OF ELECTROMAGNETIC WAVES ON A SLAB COVERED WITH GRAPHENE

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Resumo

The paper focuses on a boundary-value problem for a system of two homogeneous Helmholtz equations with mixed boundary conditions arising in the theory of electromagnetic waves scattering on structures covered with two-dimensional materials. The problem is reduced to a boundary integral equation on the whole line involving a hypersingular integral operator. Introducing new variables and sought-for function, one passes to the integral equation on segment. To find an approximate solution of the obtained equation the collocation method using Fourier-Chebyshev series to present a solution is suggested; hypersingular integrals are calculated analytically. In the main part of the paper we prove the Fredholm property of the hypersingular operator involved in the integral equation under consideration.

Sobre autores

Yu. Smirnov

Penza State University

Email: smirnovyug@mail.ru
Russia

S. Tikhov

Penza State University

Email: tik.stanislav2015@yandex.ru
Russia

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