Geodesic
Boundary inverse problem for conductive-radiative equations of heat transfer
Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 1, pp. 75-84 
P. R. Mesenev; A. Yu. Chebotarev. Boundary inverse problem for conductive-radiative equations of heat transfer. Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 1, pp. 75-84. http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The boundary inverse problem of finding the reflecting properties of the boundary region for stationary radiation-conductive heat transfer equations in the three-dimensional region is considered. The existence of a quasi-solution of the inverse problem is proved and an optimality system is obtained. An algorithm for solving a problem is presented, the effectiveness of which is illustrated by numerical examples.

[1] M. F. Modest, Radiative Heat Transfer, Academic Press, 2003

[2] Clever D. and Lang J., “Optimal control of radiative heat transfer in glass cooling with restrictions on the temperature gradient”, Optim. Control Appl. Meth., 33:2 (2012), 157–175 | DOI | MR | Zbl

[3] O. Tse, R. Pinnau, N. Siedow, “Identification of temperature dependent parameters in laser–interstitial thermo therapy”, Math. Models Methods Appl. Sci., 22:9 (2012), 1–29 | DOI | MR

[4] N. Siedow O. Tse, R. Pinnau., “Identification of temperature dependent parameters in a simplified radiative heat transfer”, Aust. J. Basic Appl. Sci., 2011, 7–14

[5] R. Pinnau O. Tse, “Optimal control of a simplified natural convection-radiation model”, Commun. Math. Sci., 2013, 679–707 | DOI | MR | Zbl

[6] G. Thomes, R. Pinnau, M. Seaid, T. Gotz, and A. Klar., Trans. Theory Stat Phys., 31:4–6 (2002), Numerical methods and optimal control for glass cooling processes | MR

[7] {Alexander Yu.} Chebotarev, {Andrey E.} Kovtanyuk, {Gleb V.} Grenkin, {Nikolai D.} Botkin, and {Karl Heinz} Hoffmann, “Nondegeneracy of optimality conditions in control problems for a radiative-conductive heat transfer model”, Applied Mathematics and Computation, 289:10 (2016), 371–380 | MR

[8] A. Chebotarev, A. Kovtanyuk, G. Grenkin, N. Botkin, and K.-H. Hoffman “Boundary optimal control problem of complex heat transfer model”, J. Math. Anal. Appl., 433:2 (2016), 1243–-1260 | DOI | MR | Zbl

[9] K. Glashoff and E. Sachs, “On theoretical and numerical aspects of the bang-bang-principle”, Numer. Math., 29:1 (1977), 93–-113 | DOI | MR | Zbl

[10] Kovtanyuk Andrey E., Chebotarev Alexander Yu., Botkin Nikolai D., and Hoffmann Karl-Heinz, “Theoretical analysis of an optimal control problem of conductive convective radiative heat transfer”, J. Math. Anal. Appl., 412 (2014), 520–-528 | DOI | MR | Zbl

[11] G. V. Grenkin, “Optimalnoe upravlenie v nestatsionarnoi modeli slozhnogo teploobmena”, Dalnevost. matem. zhurn., 14:2 (2014), 160–-172 | MR | Zbl

[12] R. V. Brizitskii, Zh. Yu. Saritskaya, “Ustoichivost reshenii ekstremalnykh zadach dlya nelineinogo uravneniya konvektsii–diffuzii–reaktsii pri uslovii Dirikhle”, Zh. vychisl. matem. i matem. fiz., 56:12 (2016), 2042–2053 | DOI | MR | Zbl

[13] G. V. Alekseev, R. V. Brizitskii, Zh. Yu. Saritskaya, “Otsenki ustoichivosti reshenii ekstremalnykh zadach dlya nelineinogo uravneniya konvektsii-diffuzii-reaktsii”, Sib. zhurn. industr. matem., 19:2 (2016), 3–16 | Zbl

[14] R. Pinnau, “Analysis of optimal boundary control for radiative heat transfer modeled by the $sp_1$-system”, Comm. Math. Sci.,, 5:4 (2007), 951–-969 | DOI | MR | Zbl

[15] A. E. Kovtanyuk, A. Yu. Chebotarev, N. D. Botkin, and Karl-Heinz Hoffman, “Unique solvability of a steady-state complex heat transfer model,”, Commun. Nonlinear Sci. Numer. Simulat., 20 (2015), 776–-784 | DOI | MR | Zbl

[16] A. D. Ioffe and V. M. Tikhomirov, Theory of extremal problems, North Holland, Amsterdam, 1979 | MR