Geodesic
Nonlocal unique solvability of a steady-state problem of complex heat transfer
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 5, pp. 816-823 Cet article a éte moissonné depuis la source Math-Net.Ru

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A boundary value problem of radiative-conductive-convective heat transfer in a threedimensional domain is proved to be uniquely solvable. An iterative algorithm is proposed for finding its solution. 
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A. E. Kovtanyuk; A. Yu. Chebotarev. Nonlocal unique solvability of a steady-state problem of complex heat transfer. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 5, pp. 816-823. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_5_a7/

[1] Modest M. F., Radiative heat transfer, Academic Press, 2003, 822 pp.

[2] Kovtanyuk A. E., Chebotarev A. Yu., “Statsionarnaya zadacha slozhnogo teploobmena”, Zh. vychisl. matem. i matem. fiz., 54:4 (2014), 191–199 | MR

[3] Andre S., Degiovanni A., “A new way of solving transient radiative-conductive heat transfer problems”, J. Heat Transfer, 120:4 (1998), 943–955 | DOI

[4] Banoczi J. M., Kelley C. T., “A fast multilevel algorithm for the solution of nonlinear systems of conductive-radiative heat transfer equations”, SIAM J. Sci. Comput., 19:1 (1998), 266–279 | DOI | MR | Zbl

[5] Thömes G., Pinnau R., Seaïd M., Götz T., Klar A., “Numerical methods and optimal control for glass cooling processes”, Trans. Theory Stat. Phys., 31:4–6 (2002), 513–529 | DOI | MR

[6] Pinnau R., Seaid M., “Simplified PN models and natural convection-radiation”, Math. in Industry, 12 (2008), 397–401 | DOI | MR | Zbl

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

[8] Kovtanyuk A. E., “Algoritmy parallelnykh vychislenii dlya zadach radiatsionno-konduktivnogo teploobmena”, Kompyuternye issledovaniya i modelirovanie, 4:3 (2012), 543–552

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

[10] Amosov A. A., “Globalnaya razreshimost odnoi nelineinoi nestatsionarnoi zadachi s nelokalnym kraevym usloviem tipa teploobmena izlucheniem”, Differents. ur-niya, 41:1 (2005), 93–104 | MR | Zbl

[11] Pinnau R., “Analysis of optimal boundary control for radiative heat transfer modelled by the $\mathrm{SP_1}$-system”, Comm. Math. Sci., 5:4 (2007), 951–969 | DOI | MR | Zbl

[12] Druet P.-E., “Existence of weak solutions to the time-dependent MHD-equations coupled to heat transfer with nonlocal radiation boundary conditions”, Nonlinear Analys. Real World Appl., 10:5 (2009), 2914–2936 | DOI | MR | Zbl

[13] Ducomet B., Necasova S., “Global Weak Solutions to the 1D Compressible Navier–Stokes Equations with Radiation”, Commun. Math. Analys., 8:3 (2010), 23–65 | MR | Zbl

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

[15] Kelley C. T., “Existence and uniqueness of solutions of nonlinear systems of conductive-radiative heat transfer equations”, Transport Theory Statist. Phys., 25:2 (1996), 249–260 | DOI | MR | Zbl

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

[17] Amosov A. A., “O razreshimosti odnoi zadachi teploobmena izlucheniem”, Dokl. AN SSSR, 245:6 (1979), 1341–1344 | MR

[18] Amosov A. A., “O predelnoi svyazi mezhdu dvumya zadachami teploobmena izlucheniem”, Dokl. AN SSSR, 246:5 (1979), 1080–1083 | MR

[19] Laitinen M. T., Tiihonen T., “Heat transfer in conducting, radiating and semitransparent materials”, Math. Meth. Appl. Sci., 21 (1998), 375–392 | 3.0.CO;2-U class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[20] Laitinen M., “Asymptotic analysis of conductive-radiative heat transfer”, Asymptotic Analys., 29:3–4 (2002), 323–342 | MR | Zbl

[21] Amosov A. A., “Stationary nonlinear nonlocal problem of radiative-conductive heat transfer in a system of opaque bodies with properties depending on the radiation frequency”, J. Math. Sci., 164:3 (2010), 309–344 | DOI | MR | Zbl

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

[23] Kovtanyuk A. E., Chebotarev A. Yu., “Statsionarnaya zadacha svobodnoi konvektsii s radiatsionnym teploobmenom”, Diff. ur-niya, 50:12 (2014), 1590–1597 | DOI | Zbl

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

[25] Kufner A., Fuchik S., Nelineinye differentsialnye uravneniya, Nauka, M., 1988 | MR

[26] Mazya V. G., “O koertsitivnosti zadachi Dirikhle v oblasti s neregulyarnoi granitsei”, Izv. vuzov. Matematika, 1973, no. 4, 64–76

[27] Khermander L., Lineinye differentsialnye operatory s chastnymi proizvodnymi, Mir, M., 1965 | MR

[28] Fursikov A. V., Emanuilov O. Yu., “Lokalnaya tochnaya upravlyaemost uravnenii Bussineska”, Vestn. RUDN. Ser. Matematika, 1996, no. 3(1), 177–194 | MR