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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 12, Pages 1863–1878
DOI: https://doi.org/10.7868/S0044466914120060 (Mi zvmmf10121) 		 
This article is cited in 25 scientific papers (total in 25 papers)

Stability estimates in the problem of cloaking material bodies for Maxwell’s equations

G. V. Alekseevab

a Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, ul. Radio 7, Vladivostok, 690041, Russia
b Far Eastern Federal University, ul. Sukhanova 8, Vladivostok, 690041, Russia
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DOI: https://doi.org/10.7868/S0044466914120060
Abstract: A control problem is considered for the three-dimensional Maxwell equations in the exterior of an impenetrable body with a boundary partly covered for cloaking. The role of the control is played by the surface impedance of the covered part of the boundary, which enters into the impedance boundary condition. The solvability of the control problem is proved, and an optimality system describing necessary conditions for an extremum is derived. An analysis of the optimality system yields sufficient conditions on the initial data that ensure the uniqueness and stability of optimal solutions for a particular cost functional.
Key words: Maxwell’s equations, mixed transmission problem, boundary impedance, control problem, optimality system, solvability, stability.
Received: 13.01.2014
Revised: 28.04.2014
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 12, Pages 1788–1803
DOI: https://doi.org/10.1134/S0965542514120069
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
Citation: G. V. Alekseev, “Stability estimates in the problem of cloaking material bodies for Maxwell’s equations”, Zh. Vychisl. Mat. Mat. Fiz., 54:12 (2014), 1863–1878; Comput. Math. Math. Phys., 54:12 (2014), 1788–1803
Citation in format AMSBIB
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    • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Æóðíàë âû÷èñëèòåëüíîé ìàòåìàòèêè è ìàòåìàòè÷åñêîé ôèçèêè Computational Mathematics and Mathematical Physics
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