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Advances in Mathematical Physics
Volume 2015, Article ID 945965, 6 pages
Research Article

Integrodifferential Equations of the Vector Problem of Electromagnetic Wave Diffraction by a System of Nonintersecting Screens and Inhomogeneous Bodies

1Department of Mathematics and Supercomputer Modeling, Penza State University, Penza 440026, Russia
2Department of Mathematics, Penza State University, Krasnaya Street 40, Penza 440026, Russia

Received 20 November 2014; Revised 8 April 2015; Accepted 15 April 2015

Academic Editor: Prabir Daripa

Copyright © 2015 Y. G. Smirnov and A. A. Tsupak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The vector problem of electromagnetic wave diffraction by a system of bodies and infinitely thin screens is considered in a quasi-classical formulation. The solution is sought in the classical sense but is defined not in the entire space but rather everywhere except for the screen edges. The original boundary value problem for Maxwell’s equations system is reduced to a system of integrodifferential equations in the regions occupied by the bodies and on the screen surfaces. The integrodifferential operator is treated as a pseudodifferential operator in Sobolev spaces and is shown to be zero-index Fredholm operator.