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

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 obtaine...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2023-11, Vol.63 (11), p.2050-2059
Main Author: Chebotarev, A. Yu
Format: Article
Language:English
Subjects:
Boundary value problems
Computational Mathematics and Numerical Analysis
Elliptic functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Optimal Control
Optimization
Radiative heat transfer
Refractivity
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542523110064