Far Eastern Mathematical Journal

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Identification of heat sources in a complex heat transfer model


Grenkin G. V.

2024, issue 2, P. 170-177
DOI: https://doi.org/10.47910/FEMJ202415


Abstract
The problem of recovering the intensities of heat sources with given volume densities and known values of average temperature is considered within the complex heat transfer model. An algorithm for the numerical solution of this problem is proposed. The conditions for the uniqueness of the solution are obtained.

Keywords:
radiative heat transfer, inverse problem, integral overdetermination.

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References

[1] Chebotarev A. Yu., Grenkin G. V., Kovtanyuk A. E., Botkin N. D., “Inverse problem with finite overdetermination for steady-state equations of radiative heat exchange”, J. Math. Anal. Appl., 460:2, (2018), 737–744.
[2] CHebotarev A. IU., “Obratnaia zadacha dlia uravneni? slozhnogo teploobmena c frenelevskimi usloviiami sopriazheniia” , ZH. vychisl. matem. i matem. fiz., 61:2, (2021), 303–311.
[3] Grenkin G. V., “Edinstvennost? resheniia obratno? zadachi dlia modeli slozhnogo teploobmena” , Sib. ?lektron. matem. izv., 21:1, (2024), 98–104.
[4] Chebotarev A. Yu., Pinnau R., “An inverse problem for a quasi-static approximate model of radiative heat transfer”, J. Math. Anal. Appl., 472:1, (2019), 314–327.
[5] Kovtanyuk A., Chebotarev A., Turova V., Sidorenko I., “An inverse problem for equations of cerebral oxygen transport”, Appl. Math. Comput., 402, (2021), 126154.
[6] Kovtanyuk A., Chebotarev A., Turova V., Sidorenko I., “Inverse problem for a linearized model of oxygen transport in brain”, 2020 Days on Diffraction (DD), 2020, 44–49.
[7] Kovtanyuk A., Chebotarev A., Turova V., Sidorenko I., “Non-stationary model of cerebral oxygen transport with unknown sources”, Mathematics, 9:8, (2021), 910.
[8] Grenkin G. V., “Upravlenie nagrevom oblasti v ramkakh modeli slozhnogo teploobmena”, Informatika i sistemy upravleniia, 2024, № 1 (79), 121–125.
[9] Grenkin G. V., “CHislennoe reshenie obratno? zadachi vosstanovleniia teplovykh istochnikov” , Territoriia novykh vozmozhnoste?. Vestnik Vladivostokskogo gosudarstvennogo universiteta, 16:2, (2024), 161–170.
[10] Urinov A. K., Azizov M. S., “Boundary value problems for a fourth order partial differential equation with an unknown right-hand part”, Lobachevskii J. Math., 42, (2021), 632–640.
[11] Baranchuk V. A., Pyatkov S. G., “On some inverse problems of recovering sources in stationary convection-diffusion models”, Lobachevskii J. Math., 44:3, (2023), 1111.
[12] Kovtanyuk A., Chebotarev A., Astrakhantseva A., “Inverse extremum problem for a model of endovenous laser ablation”, J Inverse Ill Posed Probl., 29:3, (2021), 467–476.
[13] Chebotarev A. Yu., Kovtanyuk A. E., Grenkin G. V., Botkin N. D., “Nondegeneracy of optimality conditions in control problems for a radiative-conductive heat transfer model”, Appl. Math. Comput., 289, (2016), 371–380.

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