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The Problem of Complex Heat Transfer with Cauchy-Type Conditions on a Part of the Boundary

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Abstract

The paper considers a boundary value problem for stationary equations of complex heat transfer with an undetermined boundary condition for the radiation intensity on a part of the boundary and an overdetermined condition on another part of the boundary. An optimization method for solving this problem is proposed, and an analysis of the corresponding problem of boundary optimal control is presented. It is shown that the sequence of solutions of extremum problems converges to the solution of a problem with Cauchy-type conditions. The efficiency of the algorithm is illustrated by numerical examples.

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Funding

This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00113); the Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences (IAM FEB RAS) (project no. АААА-А20-120120390006-0); and the Ministry of Education and Science of the Russian Federation (project no. 122082400001-8).

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Authors and Affiliations

  1. Far Eastern Center for Mathematical Research, Far East Federal University, 690922, Vladivostok, Russia

    P. R. Mesenev

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

    A. Yu. Chebotarev

  3. Amur State University, 675027, Blagoveshchensk, Amur oblast, Russia

    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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The authors declare that they have no conflicts of interest.

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Translated by E. Chernokozhin

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Mesenev, P.R., Chebotarev, A.Y. The Problem of Complex Heat Transfer with Cauchy-Type Conditions on a Part of the Boundary. Comput. Math. and Math. Phys. 63, 897–904 (2023). https://doi.org/10.1134/S0965542523050135

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  • DOI: https://doi.org/10.1134/S0965542523050135

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