Abstract
The solvability conditions of over-determined boundary value problems for Maxwell equations in anisotropic half-paces are obtained. The method of the Fourier integral transformation on tangent spatial variables is used in a special class of generalized functions. By the method of the over-determined boundary value problem, the integral equations of the electromagnetic wave diffraction problem by a conductive thin screen in an anisotropic medium are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
I. E. Pleshchinskaya and N. B. Pleshchinskii, ‘‘Over-determined boundary value problems for elliptical partial differential equations and their application to theory of wave diffraction,’’ Uch. Zap. Kazan. Univ. 147 (3), 4–32 (2005)
I. E. Pleshchinskaya and N. B. Pleshchinskii, ‘‘Over-determined boundary value problems for PDE and their application in the wave propagation theory,’’ Appl. Anal. 93, 2350–2359 (2014).
I. E. Pleshchinskaya and N. B. Pleshchinskii, ‘‘On mixed boundary value problems for set of partial differential equations with constant coefficients in semi-spaces,’’ Lobachevskii J. Math. 39, 1090–1098 (2018).
V. V. Nikol’skii, Electrodynamics and Radio-Wave Propagation (Nauka, Moscow, 1978) [in Russian].
E. P. Kurushin and E. I. Nefedov, Electrodynamics of Anisotropical Wave-Guides Structures (Nauka, Moscow, 1983) [in Russian].
A. F. Bourganov and N. B. Pleshchinskii, ‘‘On the structure of solutions of Vaxwell equations in anisotropical semi-spaces,’’ Issled. Prikl. Mat. 27, 59–64 (2011).
A. F. Bourganov, E. M. Karchevskiy, and N. B. Pleshchinskii, ‘‘Electromagnetic wave diffraction on the conducting thin screen placed on the isotropic and anisotropic media interface,’’ in Proceedings of the Progress in Electromagnetics Research Symposium PIERS 2013, Stockholm (2013), pp. 421–425.
I. V. Gelfand and G. E. Shilov, Generalized Functions, Vol. 2: Spaces of Fundamental and Generalized Functions (Fizmatgiz, Moscow, 1958; Am. Math. Soc., Providence, RI, 2016).
R. Mittra and S. W. Lee, Analytical Techniques in the Theory of Guided Waves (Macmillan, New York, 1971).
V. A. Ditkin and A. P. Prudnikov, Integral Transformations and Operational Calculus (Nauka, Moscow, 1974) [in Russian].
Funding
This paper has been supported by the Kazan Federal University Strategic Academic Leadership Program (‘‘PRIORITY-2030’’).
Author information
Authors and Affiliations
Corresponding authors
Additional information
(Submitted by E. E. Tyrtyshnikov)
Rights and permissions
About this article
Cite this article
Pleshchinskaya, I.E., Pleshchinskii, N.B. Maxwell Equations in Anisotropic Half-Space and Integral Equations of Problem of Electromagnetic Wave Diffraction by Screen. Lobachevskii J Math 43, 1251–1259 (2022). https://doi.org/10.1134/S1995080222080273
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080222080273