The problem of radiative heat transfer without boundary conditions for the intensity of radiation
A. Yu. Chebotarevab, A. G. Kolobova, T. V. Paka
a Far Eastern Federal University, Vladivostok
b Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
The stationary problem of radiation-diffusion heat transfer in three-\linebreak dimensional domain within the $P_1$ - approximations of the radiation transfer equation is considered. The boundary conditions for the intensity of radiation are not specified, but there is an additional boundary condition for the temperature field. The non-local solvability of the problem is established and it is shown that the set of solutions is homeomorphic to a finite-dimensional compact. Submitted condition uniqueness of the solution. The conditions for the uniqueness of the solution are presented.
radiation heat transfer, diffusion approximation, non-local solvability.
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MSC: Primary 35J61; Secondary 35Q79
A. Yu. Chebotarev, A. G. Kolobov, T. V. Pak, “The problem of radiative heat transfer without boundary conditions for the intensity of radiation”, Dal'nevost. Mat. Zh., 19:1 (2019), 119–124
Citation in format AMSBIB
\by A.~Yu.~Chebotarev, A.~G.~Kolobov, T.~V.~Pak
\paper The problem of radiative heat transfer without boundary conditions for the intensity of radiation
\jour Dal'nevost. Mat. Zh.
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