Unique solvability of the subdifferential boundary value problem for the complex heat transfer equations |
Chebotarev A.Yu., Grenkin G.V., Kovtanyuk A.E. |
2016, issue 2, P. 229-236 |
Abstract |
A model of the process of radiation-conductive heat transfer with the multi-valued dependence of emissivity on the radiation intensity is considered. The unique solvability of the subdifferential boundary value problem for the complex heat transfer equations in a three-dimensional domain is proved. |
Keywords: radiation heat transfer, subdifferential boundary conditions, non-local unique solvability |
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References |
[1] Modest M.F., Radiative Heat Transfer, Academic Press, 2003. [2] A.E. Kovtaniuk, A.Iu. Chebotarev, “Statsionarnaia zadacha slozhnogo teploobmena”, Zh. vychisl. matem. fiz., 54:4 (2014), 191–199. [3] A.E. Kovtanyuk, A.Yu. Chebotarev, “An iterative method for solving a complex heat transfer problem”, Appl. Math. Comput., 219 (2013), 9356–9362. [4] A.E. Kovtanyuk, A.Yu. Chebotarev, N.D. Botkin, K.-H. Hoffmann, “Solvability of P1 approximation of a conductive-radiative heat transfer problem”, Appl. Math. Comput., 249 (2014), 247–252. [5] 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. [6] A.E. Kovtaniuk, A.Iu. Chebotarev, “Statsionarnaia zadacha svobodnoi konvektsii s radiatsionnym teploobmenom”, Differentsial'nye uravneniia, 50:12 (2014), 1590–1597. [7] G.V. Grenkin, A.Iu. Chebotarev, “Ustoichivost' statsionarnykh reshenii diffuzionnoi modeli slozhnogo teploobmena”, Dal'nevostochnyi matematicheskii zhurnal, 14:1 (2014), 18–32. [8] G.V. Grenkin, A.Iu. Chebotarev, “Nestatsionarnaia zadacha slozhnogo teploobmena”, Zh. vychisl. matem. fiz., 54:11 (2014), 1806–1816. [9] A.E. Kovtanyuk, A.Yu. Chebotarev, N.D. Botkin, K.-H. Hoffmann, “Unique solvability of a steady-state complex heat transfer model”, Communications in Nonlinear Science and Numerical Simulation, 20:2 (2015), 776–784. [10] G.V. Grenkin, A.Iu. Chebotarev, “Neodnorodnaia nestatsionarnaia zadacha slozhnogo teploobmena”, Sibirskie elektronnye matematicheskie izvestiia, 12:11 (2015), 562–576. [11] G.V. Grenkin, A.Iu. Chebotarev, “Nestatsionarnaia zadacha svobodnoi konvektsii s radiatsionnym teploobmenom”, Zh. vychisl. matem. fiz., 56:2 (2016), 275–282. [12] A.A. Amosov, “Global'naia razreshimost' odnoi nelineinoi nestatsionarnoi zadachi s nelokal'nym kraevym usloviem tipa teploobmena izlucheniem”, Differentsial'nye uravneniia, 41:1 (2005), 93–104. [13] P.-E. Druet, “Existence of weak solutions to the time-dependent MHD-equations coupled to heat transfer with nonlocal radiation boundary conditions”, Nonlinear Anal. Real World Appl., 10:5 (2009), 2914–2936. [14] 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. [15] A.A. Amosov, “O razreshimosti odnoi zadachi teploobmena izlucheniem”, Dokl. AN SSSR, 245:6 (1979), 1341–1344. [16] A.A. Amosov, “Stationary nonlinear nonlocal problem of radiative-conductive heat transfer in a system of opaque bodies with properties depending on the radiation frequency”, Journal of Mathematical Sciences, 164:3 (2010), 309–344. [17] A.A. Amosov, “Nonstationary nonlinear nonlocal problem of radiative-conductive heat transfer in a system of opaque bodies with properties depending on the radiation frequency”, Journal of Mathematical Sciences, 165:1 (2010), 1–41. [18] R. Pinnau, “Analysis of Optimal Boundary Control for Radiative Heat Transfer Modelled by the SP1-System”, Comm. Math. Sci., 5:4 (2007), 951–969. [19] 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 (2014), 520–528. [20] G.V. Grenkin, “Optimal'noe upravlenie v nestatsionarnoi zadache slozhnogo teploobmena”, Dal'nevostochnyi matematicheskii zhurnal, 14:2 (2014), 160–172. [21] G.V. Grenkin, A.E. Kovtanyuk, A.Yu. Chebotarev, N.D. Botkin, K.-H. Hoffmann, “Boundary optimal control problem of complex heat transfer model”, J. Math. Anal. Appl., 433 (2016), 1243–1260. [22] A.E. Kovtanyuk, A.Yu. Chebotarev, N.D. Botkin, K.-H. Hoffmann, “Optimal boundary control of a steady-state heat transfer model accounting for radiative effects”, J. Math. Anal. Appl., 439 (2016), 678–689. [23] A.Yu. Chebotarev, A.E. Kovtanyuk, G.V. Grenkin, N.D. Botkin, K.-H. Hoffmann, “Nondegeneracy of optimality conditions in control problems for a radiative-conductive heat transfer model”, Applied Mathematics and Computation, 289 (2016), 371–380. [24] G.V. Grenkin, “Algoritm resheniia zadachi granichnogo optimal'nogo upravleniia v modeli slozhnogo teploobmena”, Dal'nevostochnyi matematicheskii zhurnal, 16:1 (2016), 24–38. [25] G.V. Grenkin, A.Iu. Chebotarev, “Upravlenie slozhnym teploobmenom pri sozdanii ekstremal'nykh polei”, Zh. vychisl. matem. fiz., 56:10 (2016), 1725–1732. [26] Lions Zh.-L., Nekotorye metody resheniia nelineinykh kraevykh zadach, M.: Mir, 1972. [27] A.Iu. Chebotarev, “Variatsionnye neravenstva dlia operatora tipa Nav'e-Stoksa i odnostoronnie zadachi dlia uravnenii viazkoi teploprovodnoi zhidkosti”, Matematicheskie zametki, 70:2 (2001), 296–307. |