Geodesic
A nonhomogeneous nonstationary complex heat transfer problem
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 562-576.

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A nonhomogeneous nonstationary problem of radiative-conductive-convective heat tranfer in a three-dimensional domain is investigated in the framework of the diffusion $P_1$-approximation of the radiative heat transfer equation. The unique solvability of the problem is proved.
Keywords: radiative heat transfer, unique solvability.
Mots-clés : diffusion approximation 
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G. V. Grenkin; A. Yu. Chebotarev. A nonhomogeneous nonstationary complex heat transfer problem. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 562-576. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a62/

[1] G. V. Grenkin, A. Yu. Chebotarev, “A nonstationary problem of complex heat transfer”, Comput. Math. Math. Phys., 54:11 (2014), 1737–1747 | DOI | MR

[2] G. V. Grenkin, A. Yu. Chebotarev, “The stability of steady-state solutions of the diffusion complex heat transfer model”, Far Eastern Mathematical Journal, 14:1 (2014), 18–32 (In Russian)

[3] R. Pinnau, “Analysis of optimal boundary control for radiative heat transfer modelled by the SP$_1$-system”, Commun. Math. Sci., 5:4 (2007), 951–969 | DOI | MR | Zbl

[4] O. Tse, R. Pinnau, “Optimal control of a simplified natural convection-radiation model”, Commun. Math. Sci., 11:3 (2013), 679–707 | DOI | MR | Zbl

[5] A. E. Kovtanyuk, A. Yu. Chebotarev, “An iterative method for solving a complex heat transfer problem”, Appl. Math. Comput., 219:17 (2013), 9356–9362 | DOI | MR | Zbl

[6] A. E. Kovtanyuk, A. Yu. Chebotarev, “Steady-state problem of complex heat transfer”, Comput. Math. Math. Phys., 54:4 (2014), 719–726 | DOI | MR | Zbl

[7] A. E. Kovtanyuk, A. Yu. Chebotarev, “Stationary free convection problem with radiative heat exchange”, Differ. Equ., 50:12 (2014), 1592–1599 | DOI | Zbl

[8] A. E. Kovtanyuk, A. Yu. Chebotarev, N. D. Botkin, K.-H. Hoffmann, “Theoretical analysis of an optimal control problem of conductive-convective-radiative heat transfer”, J. Math. Anal. Appl., 412:1 (2014), 520–528 | DOI | MR | Zbl

[9] A. E. Kovtanyuk, A. Yu. Chebotarev, N. D. Botkin, K.-H. Hoffmann, “The unique solvability of a complex 3D heat transfer problem”, J. Math. Anal. Appl., 409:2 (2014), 808–815 | DOI | MR | Zbl

[10] A. E. Kovtanyuk, A. Yu. Chebotarev, N. D. Botkin, K.-H. Hoffmann, “Solvability of P$_1$ approximation of a conductive-radiative heat transfer problem”, Appl. Math. Comput., 249 (2014), 247–252 | DOI | MR

[11] A. E. Kovtanyuk, A. Yu. Chebotarev, N. D. Botkin, K.-H. Hoffmann, “Unique solvability of a steady-state complex heat transfer model”, Commun. Nonlinear Sci. Numer. Simul., 20:3 (2015), 776–784 | DOI | MR | Zbl

[12] R. Backofen, T. Bilz, A. Ribalta, A. Voigt, “SP$_N$-approximations of internal radiation in crystal growth of optical materials”, J. Cryst. Growth, 266:1–3 (2004), 264–270 | DOI

[13] A. Klar, J. Lang, M. Seaïd, “Adaptive solution of SP$_N$-approximations to radiative heat transfer in glass”, Int. J. Therm. Sci., 44:11 (2005), 1013–1023 | DOI

[14] A. E. Kovtanyuk, N. D. Botkin, K.-H. Hoffmann, “Numerical simulations of a coupled radiative-conductive heat transfer model using a modified Monte Carlo method”, Int. J. Heat Mass Tran., 55:4 (2012), 649–654 | DOI | MR | Zbl

[15] E. Zeidler, Nonlinear functional analysis and its applications, v. II/A, Linear monotone operators, Springer, New York, 1990 | MR

[16] J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Paris, 1969 | MR

[17] V. A. Trenogin, Functional analysis, Fizmatlit, M., 2002 (In Russian)

[18] D. Kinderlehrer, G. Stampacchia, An introduction to variational inequalities and their applications, Academic Press, New York, 1980 | MR | Zbl

[19] H. Berninger, “Non-overlapping domain decomposition for the Richards equation via superposition operators”, Domain Decomposition Methods in Science and Engineering XVIII, Lecture Notes in Computational Science and Engineering, 70, Springer, 2009, 169–176 | DOI | MR | Zbl