Abstract
For the boundary value problem of diffraction of an external disturbance by a local penetrable body with smooth surface, we construct an integral representation of the solution based on a linear combination of single and double layer potentials with densities distributed over a common auxiliary interior surface. A complete mathematical justification of this representation is given.
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REFERENCES
Anisimkin, V.I. and Voronova, N.V., Features of normal higher-order acoustic wave generation in thin piezoelectric plates, Acoust. Phys., 2020, vol. 66, no. 1, pp. 1–4.
Grishina, N.V., Eremin, Yu.A., and Sveshnikov, A.G., New concept of the discrete sources method in electromagnetic scattering problems, Math. Models Comput. Simul., 2015, vol. 8, pp. 175–182.
Bettelheim, F.A., Light scattering in lens research: an essay on accomplishments and promises, Exp. Eye Res., 2004, vol. 79, no. 6, pp. 747–752.
Dmitriev, V.I. and Zakharov, E.V., Metod integral’nykh uravnenii v vychislitel’noi elektrodinamike (Method of Integral Equations in Computational Electrodynamics), Moscow: MAKS Press, 2008.
Kupradze, V.D., On the approximate solution of problems in mathematical physics, Russ. Math. Surv., 1967, vol. 22, no. 2, pp. 58–108.
Martin, P.A. and Ola, P., Boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle, Proc. R. Soc., 1993, vol. 123, pp. 185–208.
Zakharov, E.V., Setukha, A.V., and Bezobrazova, E.N., Method of hypersingular integral equations in a three-dimensional problem of diffraction of electromagnetic waves on a piecewise homogeneous dielectric body, Differ. Equations, 2015, vol. 51, no. 9, pp. 1197–1210.
Eremin, Yu.A., Integro-functional representations with complex support for wave fields, Differ. Equations, 2009, vol. 45, no. 9, pp. 1379–1386.
Eremin, Yu.A., Allowance for the nonlocal interaction of plasmonic particles in the discrete sources method, Dokl. Math., 2015, vol. 91, pp. 222–226.
Tsitsas, N.L., Zouros, G.P., Fikioris, G., and Leviatan, Y., On methods employing auxiliary sources for 2-D electromagnetic scattering by non-circular shapes, IEEE Trans. AP, 2018, vol. 66, no. 10, pp. 5443–5452.
Korn, G.A. and Korn, T.M., Mathematical Handbook for Scientists and Engineers, New York–San Francisco–Toronto–London–Sydney: McGraw-Hill, 1968. Translated under the title: Spravochnik po matematike, Moscow: Nauka, 1977.
Trenogin, V.A., Funktsional’nyi analiz (Functional Analysis), Moscow: Nauka, 1985.
Bers, L., John, F., and Schechter, M., Partial Differential Equations, New York–London–Sydney: Interscience, 1964. Translated under the title: Uravneniya s chastnymi proizvodnymi, Moscow: Mir, 1966.
Colton, D. and Kress, R., Inverse Acoustic and Electromagnetic Scattering Theory, Berlin: Springer, 2013, pp. 200–208.
Doicu, A., Eremin, Yu., and Wriedt, T., Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources, San Diego: Academic Press, 2000, pp. 35–38.
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Translated by V. Potapchouck
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Eremin, Y.A. Integral Representations of Fields in Three-Dimensional Problems of Diffraction by Penetrable Bodies. Diff Equat 56, 1148–1152 (2020). https://doi.org/10.1134/S0012266120090050
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DOI: https://doi.org/10.1134/S0012266120090050