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On the Fredholm property of the electric field equation in the vector diffraction problem for a partially screened solid

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Abstract

We consider a vector problem of diffraction of an electromagnetic wave on a partially screened anisotropic inhomogeneous dielectric body. The boundary conditions and the matching conditions are posed on the boundary of the inhomogeneity domain, and under passage through it, the medium parameters have jump changes. A boundary value problem for the system of Maxwell equations in unbounded space is studied in a semiclassical statement and is reduced to a system of integro-differential equations on the body domain and the screen surfaces. We show that the quadratic form of the problem operator is coercive and the operator itself is Fredholm with zero index.

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Authors and Affiliations

  1. Penza State University, Penza, Russia

    Yu. G. Smirnov & A. A. Tsupak

Authors
  1. Yu. G. Smirnov
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  2. A. A. Tsupak
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Correspondence to Yu. G. Smirnov.

Additional information

Original Russian Text © Yu.G. Smirnov, A.A. Tsupak, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 9, pp. 1242–1251.

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Smirnov, Y.G., Tsupak, A.A. On the Fredholm property of the electric field equation in the vector diffraction problem for a partially screened solid. Diff Equat 52, 1199–1208 (2016). https://doi.org/10.1134/S0012266116090111

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  • DOI: https://doi.org/10.1134/S0012266116090111

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