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Optimal Control of Quasi-Stationary Equations of Complex Heat Transfer with Reflection and Refraction Conditions

  • OPTIMAL CONTROL
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Abstract

The paper considers a class of optimal control problems for a nonlinear parabolic-elliptic system simulating radiative heat transfer with Fresnel matching conditions on surfaces of discontinuity of the refractive index. New estimates for the solution of the initial-boundary value problem are obtained, on the basis of which the solvability of optimal control problems is proved. Non-degenerate first-order optimality conditions are derived. The results are examplified by control problems with final, boundary, and distributed observations.

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Funding

This work was supported by the Russian Science Foundation, grant no. 23-21-00087.

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Authors and Affiliations

  1. Regional Scientific and Educational Mathematical Center, Far Eastern Federal University, 690922, Vladivostok, Russia

    A. Yu. Chebotarev

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  1. A. Yu. Chebotarev
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Correspondence to A. Yu. Chebotarev.

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The author declares that he has no conflicts of interest.

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Translated by E. Chernokozhin

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Chebotarev, A.Y. Optimal Control of Quasi-Stationary Equations of Complex Heat Transfer with Reflection and Refraction Conditions. Comput. Math. and Math. Phys. 63, 2050–2059 (2023). https://doi.org/10.1134/S0965542523110064

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  • DOI: https://doi.org/10.1134/S0965542523110064

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