Geodesic
An initial boundary value problem for the radiative transfer equation with diffusion matching conditions
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 1, pp. 75-85

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We consider the Cauchy problem for the nonstationary equation of radiative transfer with generalized matching conditions describing the diffusion reflection and refraction on the separation boundary of the media. We prove solvability of the initial boundary value problem and obtainh stabilization conditions for an unsteady solution.
Keywords: diffusion matching conditions, integro-differential equation, nonstationary equation, Cauchy problem, Hille–Yosida theorem. 
@article{SJIM_2017_20_1_a7,
     author = {I. V. Prokhorov and A. A. Sushchenko and A. Kim},
     title = {An initial boundary value problem for the radiative transfer equation with diffusion matching conditions},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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     publisher = {mathdoc},
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     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2017_20_1_a7/}
}
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I. V. Prokhorov; A. A. Sushchenko; A. Kim. An initial boundary value problem for the radiative transfer equation with diffusion matching conditions. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 1, pp. 75-85. http://geodesic.mathdoc.fr/item/SJIM_2017_20_1_a7/