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Optimal Control Problems for Complex Heat Transfer Equations with Fresnel Matching Conditions

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.

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Funding

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).

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Correspondence to A. Yu. Chebotarev.

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Translated by E. Chernokozhin

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Chebotarev, A.Y. Optimal Control Problems for Complex Heat Transfer Equations with Fresnel Matching Conditions. Comput. Math. and Math. Phys. 62, 372–381 (2022). https://doi.org/10.1134/S0965542522030058

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  • DOI: https://doi.org/10.1134/S0965542522030058

Keywords:

  • stationary equations of radiative heat transfer
  • Fresnel matching conditions
  • optimal control problems
  • optimality conditions
  • relay control