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.
Key words:
stationary equations of radiative heat transfer, Fresnel matching conditions, optimal control problems, optimality conditions, relay control.
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).
This publication is cited in the following 9 articles:
R. V. Brizitskii, N. N. Maksimova, “O edinstvennosti i ustoichivosti reshenii zadach upravleniya dlya modeli dreifa-diffuzii elektronov”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 35:1 (2025), 27–46
R. V. Brizitskii, A. A. Donchak, “Multiplicative Control Problem for a Nonlinear Reaction–Diffusion Model”, Comput. Math. and Math. Phys., 64:1 (2024), 56
A. Yu. Chebotarev, “Ekstremalnye zadachi dlya kvazistatsionarnykh uravnenii slozhnogo teploobmena s frenelevskimi usloviyami sopryazheniya”, Dalnevost. matem. zhurn., 24:1 (2024), 133–140
R. V. Brizitskii, N. N. Maksimova, “MULTIPLICATIVE CONTROL PROBLEMS FOR THE DIFFUSION-DRIFT CHARGING MODEL OF AN INHOMOGENEOUS POLAR DIELECTRIC”, Differencialʹnye uravneniâ, 60:5 (2024)
R. V. Brizitskii, A. A. Donchak, “Zadacha multiplikativnogo upravleniya dlya nelineinoi modeli reaktsii–diffuzii”, Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, 64:1 (2024)
R. V. Brizitskii, N. N. Maksimova, “Multiplicative Control Problems for the Diffusion–Drift Charging
Model of an Inhomogeneous Polar Dielectric”, Diff Equat, 60:5 (2024), 614
A. Yu. Chebotarev, “Optimal control of quasi-stationary equations of complex heat transfer with reflection and refraction conditions”, Comput. Math. Math. Phys., 63:11 (2023), 2050–2059
R. V Brizitskiy, P. A Maksimov, “Ob ustoychivosti resheniy zadach upravleniya dlya nelineynoy modeli reaktsii-diffuzii-konvektsii”, Differentsialnye uravneniya, 59:3 (2023), 409
R. V. Brizitskii, P. A. Maksimov, “On the Stability of Solutions to Control Problems for a Nonlinear Reaction–Diffusion–Convection Model”, Diff Equat, 59:3 (2023), 414
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