Geodesic
Extremal problems for quasi-stationary equations of complex heat transfer with Fresnel coupling conditions
Dalʹnevostočnyj matematičeskij žurnal, Tome 24 (2024) no. 1, pp. 133-140.

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The analysis of optimal control problems for a nonlinear system simulating unsteady complex heat transfer with Fresnel coupling conditions on refractive index discontinuity surfaces is considered. Estimates for the solution of the initial-boundary value problem, the solvability of control problems are presented, and optimality conditions leading to the relay nature of optimal control are derived. 
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A. Yu. Chebotarev. Extremal problems for quasi-stationary equations of complex heat transfer with Fresnel coupling conditions. Dalʹnevostočnyj matematičeskij žurnal, Tome 24 (2024) no. 1, pp. 133-140. http://geodesic.mathdoc.fr/item/DVMG_2024_24_1_a11/

[1] Chebotarev Alexander Yu., Grenkin Gleb V., Kovtanyuk Andrey and Botkin Nikolai and Hoffmann Karl-Heinz E. D., “Diffusion approximation of the radiative-conductive heat transfer model with Fresnel matching conditions”, Communications in Nonlinear Science and Numerical Simulation, 57 (2018), 290–298, Elsevier {BV} | DOI | MR

[2] Pinnau R., “Analysis of optimal boundary control for radiative heat transfer modeled by $SP_1$-system”, Commun. Math. Sci., 5:4 (2007), 951–969 | DOI | MR | Zbl

[3] Chebotarev A. Yu., “Inhomogeneous Boundary Value Problem for Complex Heat Transfer Equations with Fresnel Matching Conditions”, Differential Equations, 56:12 (2020), 1613–1618 | DOI | MR

[4] Chebotarev A. Yu., “Obratnaya zadacha dlya uravnenii slozhnogo teploobmena s frenelevskimi usloviyami sopryazheniya”, Zh. vychisl. matem. i matem. fiz., 61:2 (2021), 303–311 | DOI | Zbl

[5] Chebotarev A. Yu., “Zadachi optimalnogo upravleniya dlya uravnenii slozhnogo teploobmena s frenelevskimi usloviyami sopryazheniya”, Zh. vychisl. matem. i matem. fiz., 62:3 (2022), 381–390 | DOI | Zbl

[6] Chebotarev A. Y., Kovtanyuk A. E., “Quasi-static diffusion model of complex heat transfer with reflection and refraction conditions”, J. Math. Anal. Appl., 507:125745 (2022) | MR | Zbl

[7] Chebotarev A. Yu., “Neodnorodnaya zadacha dlya kvazistatsionarnykh uravnenii slozhnogo teploobmena s usloviyami otrazheniya i prelomleniya”, Zh. vychisl. matem. i matem. fiz., 63:3 (2023), 118–126

[8] Amosov A. A., “Unique Solvability of a Nonstationary Problem of Radiative - Conductive Heat Exchange in a System of Semitransparent Bodies”, Russian J. of Math. Phys., 23 (2016), 309–334 | DOI | MR | Zbl

[9] Amosov A. A., “Nonstationary problem of complex heat transfer in a system of semitransparent bodies with boundary-value conditions of diffuse reflection and refraction of radiation”, Journal of Mathematical Sciences, 233:6 (2018), 777–806 | DOI | MR | Zbl

[10] Chebotarev A. Yu., “Optimalnoe upravlenie kvazistatsionarnymi uravneniyami slozhnogo teploobmena s usloviyami otrazheniya i prelomleniya”, Zh. vychisl. matem. i matem. fiz., 63:11 (2023), 1829–1838 | DOI