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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 2, Pages 265–282 (Mi smj2194)  

This article is cited in 2 scientific papers (total in 2 papers)

The energy method for constructing time-harmonic solutions to the Maxwell equations

V. V. Denisenkoab

a Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia
b Siberian Federal University, Krasnoyarsk, Russia
Full-text PDF (321 kB) Citations (2)
References:
Abstract: We propose some minimum principle for an energy functional in an elliptic boundary value problem that arises in constructing time-harmonic solutions to the Maxwell equations. We suggest the potentials other than the vector and scalar potentials, used in the mathematical modeling of electromagnetic fields since the operators of traditional problems are not sign definite, which complicates constructions of iterative solution methods. We consider the problem in a parallelepiped whose boundary is ideally conducting. For nonresonant frequencies we prove that the operator of the boundary value problem is positive definite, propose a minimum principle for a quadratic energy functional, and prove the existence and uniqueness of generalized solutions.
Keywords: energy functional, elliptic equation, electrodynamics.
Received: 15.07.2010
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 2, Pages 207–221
DOI: https://doi.org/10.1134/S0037446611020030
Bibliographic databases:
Document Type: Article
UDC: 517.9+537.8
Language: Russian
Citation: V. V. Denisenko, “The energy method for constructing time-harmonic solutions to the Maxwell equations”, Sibirsk. Mat. Zh., 52:2 (2011), 265–282; Siberian Math. J., 52:2 (2011), 207–221
Citation in format AMSBIB
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\paper The energy method for constructing time-harmonic solutions to the Maxwell equations
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\pages 265--282
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\jour Siberian Math. J.
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\pages 207--221
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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