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Analysis of an Optimization Method for Solving the Problem of Complex Heat Transfer with Cauchy Boundary Conditions

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Abstract

An optimization method is proposed for solving a boundary value problem with Cauchy conditions for the equations of radiative-conductive heat transfer in the \({{P}_{1}}\)-approximation of the radiative transfer equation. Theoretical analysis of the corresponding problem of boundary optimal control is carried out. It is shown that a sequence of solutions of extremal problems converges to the solution of the boundary value problem with the Cauchy conditions for temperature. The results of theoretical analysis are illustrated with numerical examples.

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Funding

This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00113) and the Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences (topic no. 075-01095-20-00).

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Authors and Affiliations

  1. Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, 690041, Vladivostok, Russia

    P. R. Mesenev & A. Yu. Chebotarev

  2. Regional Scientific and Educational Mathematical Center “Far Eastern Center for Mathematical Research”, 690922, Vladivostok, Russia

    P. R. Mesenev & A. Yu. Chebotarev

Authors
  1. P. R. Mesenev
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  2. A. Yu. Chebotarev
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Correspondence to A. Yu. Chebotarev.

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Translated by E. Chernokozhin

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Mesenev, P.R., Chebotarev, A.Y. Analysis of an Optimization Method for Solving the Problem of Complex Heat Transfer with Cauchy Boundary Conditions. Comput. Math. and Math. Phys. 62, 33–41 (2022). https://doi.org/10.1134/S0965542522010092

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  • DOI: https://doi.org/10.1134/S0965542522010092

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