Geodesic
Nonstationary problem of complex heat transfer in a~system of semitransparent bodies with radiation diffuse reflection and refraction boundary-value conditions
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 2, Tome 59 (2016), pp. 5-34

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We consider a nonstationary initial-boundary value problem describing complex (radiative-conductive) heat transfer in a system of semitransparent bodies. To describe radiation propagation, we use the transport equation with radiation diffuse reflection and refraction boundary-value conditions. We take into account that the radiation intensity and optical properties of bodies depend on the radiation frequency. The unique solvability of a weak solution is established. The comparison theorem is proved. A priori estimates of a weak solution are obtained as well as its regularity. 
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     author = {A. A. Amosov},
     title = {Nonstationary problem of complex heat transfer in a~system of semitransparent bodies with radiation diffuse reflection and refraction boundary-value conditions},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {5--34},
     publisher = {mathdoc},
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     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2016_59_a0/}
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A. A. Amosov. Nonstationary problem of complex heat transfer in a~system of semitransparent bodies with radiation diffuse reflection and refraction boundary-value conditions. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 2, Tome 59 (2016), pp. 5-34. http://geodesic.mathdoc.fr/item/CMFD_2016_59_a0/