Boundary integral equations of the third boundary-value problem for the Helmholtz equation in R2+ with plane-parallel slits

TitleBoundary integral equations of the third boundary-value problem for the Helmholtz equation in R2+ with plane-parallel slits
Publication TypeJournal Article
Year of Publication2014
AuthorsGandel’, Yu.V, Dushkin, VD
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2014.08.014
Issue8
SectionMathematics
Pagination14-19
Date Published8/2014
LanguageRussian
Abstract

The systems of boundary integral equations of the third boundary-value problems for the Helmholtz equation have been obtained by the method of the parametric representations of integral operators. These boundary-value problems arise at the scattering of polarized electromagnetic waves on a shielded multilayer parallel finite system of impedance tapes.

Keywordsboundary integral equations, Helmholtz equation
References: 

1. Akhiezer N. I. Lectures on integral transforms Providence: Amer. Math. Soc., 1988.
2. Gandel Yu. V. Parametric representations of singular integral transformations and boundary value problems of mathematical physics. In: Nonlinear boundary value problems of mathematical physics and their applications, Kyiv: Institute of Mathematics NAS of Ukraine, 1995: 65–66 (in Russian).
3. Gandel’ Yu. V. Parametric representations of integral and pseudodifferential operators in diffraction problems. Proceedings of the 10th Intern. conf. on Math. Methods in Electromagnetic Theory, Dnepropetrovsk, Ukraine, Sept. 14–17, Dnepropetrovsk, 2004: 57–62.
4. Gandel’ Yu. V. J. Math. Sci., 2010, 171, No 1: 74–88.
5. Lifanov I. K. Singular integral equations and discrete vortices, Utrecht; Tokyo: VSP, 1996.
6. Gandel Yu. V., Dushkin V. D. Mathematical models of two-dimensional diffraction problems: Singular integral equations and numerical methods of discrete features, Kharkiv: Akad. VV MVD Ukrainy, 2012 (in Russian).
7. Nesvit K. V. Int. J. Math. Models and Meth. Appl. Sci., 2013, 7, No 11: 897–906.
8. Gandel Yu. V., Kravchenko V. F., Pustovoit V. I. Dokl. AN, 1996, 351, No 4: 57–63 (in Russian).