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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 4, Pages 702–709 (Mi zvmmf10564)  

On the unique existence of the classical solution to the problem of electromagnetic wave diffraction by an inhomogeneous lossless dielectric body

Yu. G. Smirnov, A. A. Tsupak

Penza State University, Penza, Russia

Abstract: A vector problem of electromagnetic wave diffraction by an inhomogeneous volumetric body is considered in the classical formulation. The uniqueness theorem for the solution to the boundary value problem for the system of Maxwell’s equations is proven in the case when the permittivity is real and varies jumpwise on the boundary of the body. A vector integro-differential equation for the electric field is considered. It is shown that the operator of the equation is continuously invertible in the space of square-summable vector functions.

Key words: vector electromagnetic wave diffraction problem, Maxwell's equation, boundary value problem, inhomogeneous lossless scatterer, integro-differential equations.

Funding Agency Grant Number
Russian Science Foundation 14-11-00344


DOI: https://doi.org/10.7868/S0044466917040111

Full text: PDF file (116 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:4, 698–705

Bibliographic databases:

UDC: 519.634
Received: 28.02.2016
Revised: 22.09.2016

Citation: Yu. G. Smirnov, A. A. Tsupak, “On the unique existence of the classical solution to the problem of electromagnetic wave diffraction by an inhomogeneous lossless dielectric body”, Zh. Vychisl. Mat. Mat. Fiz., 57:4 (2017), 702–709; Comput. Math. Math. Phys., 57:4 (2017), 698–705

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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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