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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 3, Pages 381–390
DOI: https://doi.org/10.31857/S004446692203005X (Mi zvmmf11368) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Optimal control

Optimal control problems for complex heat transfer equations with Fresnel matching conditions

A. Yu. Chebotarev

Institute of Applied Mathematics, Far-Eastern Branch, Russian Academy of Sciences, 690041, Vladivostok, Russia
Citations (8)
DOI: https://doi.org/10.31857/S004446692203005X
Abstract: A class of optimal control problems for a system of nonlinear elliptic equations simulating radiative heat transfer with Fresnel matching conditions on the surfaces of discontinuity of the refractive index is considered. Based on estimates for the solution of the boundary value problem, the solvability of the optimal control problems is proved. The existence and uniqueness of the solution of a linearized problem with the matching conditions is analyzed, and the nondegeneracy of the optimality conditions is proved. As an example, a control problem with boundary observation is considered and the relay-like character of the optimal control is shown.
Key words: stationary equations of radiative heat transfer, Fresnel matching conditions, optimal control problems, optimality conditions, relay control.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00113а
Ministry of Education and Science of the Russian Federation 075-02-2020-1482-1
This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00113a) and the Ministry of Education and Science of the Russian Federation (additional agreement no. 075-02-2020-1482-1).
Received: 13.04.2021
Revised: 31.05.2021
Accepted: 09.10.2021
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 3, Pages 372–381
DOI: https://doi.org/10.1134/S0965542522030058
Bibliographic databases:
Document Type: Article
UDC: 517.977.5
Language: Russian
Citation: A. Yu. Chebotarev, “Optimal control problems for complex heat transfer equations with Fresnel matching conditions”, Zh. Vychisl. Mat. Mat. Fiz., 62:3 (2022), 381–390; Comput. Math. Math. Phys., 62:3 (2022), 372–381
Citation in format AMSBIB
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\pages 372--381
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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