FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Finding the source intensity in the radiative heat transfer model by integral overdetermination |
Chebotarev A.Yu., Grenkin G.V. |
2019, issue 1, P. 88-95 |
Abstract |
| The quasi-static problem of radiation-diffusion heat transfer in three-dimensional domain is considered. It is required to find the intensity of thermal sources and the corresponding temperature and radiation fields according to the additional integral condition. Sufficient conditions for non-local unique solvability of the inverse problem are found. The theoretical analysis is illustrated by numerical examples. |
Keywords: quasi-static equations of radiative heat transfer, inverse problem, non-local unique solvability, numerical simulation |
Download the article (PDF-file) |
References |
| [1] Modest M.F., Radiative Heat Transfer, Academic Press, 2003. [2] 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. [3] R. Pinnau, “Analysis of Optimal Boundary Control for Radiative Heat Transfer Modelled by the SP1 -System”, Comm. Math. Sci., 5:4, (2007), 951–969. [4] 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. [5] 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. [6] A.E. Kovtanyuk, A.Yu. Chebotarev, “An iterative method for solving a complex heat transfer problem”, Appl. Math. Comput., 219, (2013), 9356–9362. [7] A.E. Kovtaniuk, A.Iu. Chebotarev, “Statsionarnaia zadacha slozhnogo teploobmena”, Zh. vychisl. matem. fiz., 54:4, (2014), 191–199. [8] 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. [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. [10] A.E. Kovtaniuk, A.Iu. Chebotarev, “Statsionarnaia zadacha svobodnoi konvektsii s radiatsionnym teploobmenom”, Differentsial'nye uravneniia, 50:12, (2014), 1590–1597. [11] G.V. Grenkin, A.Iu. Chebotarev, “Ustoichivost' statsionarnykh reshenii diffuzionnoi modeli slozhnogo teploobmena”, Dal'nevostochnyi matematicheskii zhurnal, 14:1, (2014), 18–32. [12] G.V. Grenkin, A.Iu. Chebotarev, “Nestatsionarnaia zadacha slozhnogo teploobmena”, Zh. vychisl. matem. fiz., 54:11, (2014), 1806–1816. [13] 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. [14] G.V. Grenkin, “Optimal'noe upravlenie v nestatsionarnoi zadache slozhnogo teploobmena”, Dal'nevostochnyi matematicheskii zhurnal, 14:2, (2014), 160–172. [15] G.V. Grenkin, A.Iu. Chebotarev, “Neodnorodnaia nestatsionarnaia zadacha slozhnogo teploobmena”, Sibirskie elektronnye matematicheskie izvestiia, 12:11, (2015), 562–576. [16] G.V. Grenkin, A.Iu. Chebotarev, “Nestatsionarnaia zadacha svobodnoi konvektsii s radiatsionnym teploobmenom”, Zh. vychisl. matem. fiz., 56:2, (2016), 275–282. [17] 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. [18] 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. [19] 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. [20] G.V. Grenkin, “Algoritm resheniia zadachi granichnogo optimal'nogo upravleniia v modeli slozhnogo teploobmena”, Dal'nevostochnyi matematicheskii zhurnal, 16:1, (2016), 24–38. [21] G.V. Grenkin, A.Iu. Chebotarev, “Upravlenie slozhnym teploobmenom pri sozdanii ekstremal'nykh polei”, Zh. vychisl. matem. fiz., 56:10, (2016), 1725–1732. [22] A.E. Kovtaniuk, A.Iu. Chebotarev, “Nelokal'naia odnoznachnaia razreshimost' statsionarnoi zadachi slozhnogo teploobmena”, Zh. vychisl. matem. fiz., 56:5, (2016), 816–823. [23] A.Yu. Chebotarev, G.V. Grenkin, A.E. Kovtanyuk, “Inhomogeneous steady-state problem of complex heat transfer”, ESAIM Math. Model. Numer. Anal., 51:6, (2017), 2511–2519. [24] A.Yu. Chebotarev, G.V. Grenkin, A.E. Kovtanyuk, N.D. Botkin, K.-H. Hoffmann, “Inverse problem with finite overdetermination for steady-state equations of radiative heat exchange”, J. Math. Anal. Appl., 460:2, (2018), 737–744. [25] A.Yu. Chebotarev, R. Pinnau, “An inverse problem for a quasi-static approximate model of radiative heat transfer”, J. Math. Anal. Appl., 472:1, (2019), 737–744. |