Unique solvability of a stationary radiative–conductive heat transfer problem in a semitransparent body with absolutely black inclusions

Амосов, А. А.

doi:10.1007/s00033-021-01535-5

Cited by 6 publications

(2 citation statements)

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“…In this direction, as far as the author knows, there are only articles. [1][2][3][4] The article 1 established the unique solvability of complex heat transfer problem in a convex absolutely black body containing semitransparent inclusions. This article establishes the unique solvability of a nonstationary variant of this problem.…”

Section: Introductionmentioning

confidence: 99%

“…At the same time, the problems of radiative–conductive heat transfer in systems consisting of both opaque and of semitransparent for radiation bodies remain as yet unexplored. In this direction, as far as the author knows, there are only articles 1–4 . The article 1 established the unique solvability of complex heat transfer problem in a convex absolutely black body containing semitransparent inclusions.…”

Section: Introductionmentioning

confidence: 99%

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Nonstationary radiative–conductive heat transfer problem in an absolutely black body with semitransparent inclusions

Амосов

2022

Math Methods in App Sciences

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We consider a nonstationary initial-boundary value problem governing a radiative-conductive heat transfer in an absolutely black body with semitransparent inclusions. To describe the radiative transfer, the integro-differential radiative transfer equation is used. We do not take into account the dependence of the radiation intensity and the properties of semitransparent materials on the radiation frequency. We proved at the first time the unique solvability of this problem. In addition, we proved the stability of solutions with respect to data, established a comparison theorem and results on improving the properties of solutions with an increasing on the summability of the data.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%