Geodesic
Initial-boundary value problem for a radiative transfer equation with generalized matching conditions
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1036-1056

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We consider the Cauchy problem for a non-stationary radiative transfer equation in a three-dimensional multicomponent medium with generalized matching conditions. These matching condition describe Fresnel and diffuse reflection and refraction at the interfaces. The existence and uniqueness of a solution of the initial-boundary value problem is proved. We construct a Monte-Carlo numerical method designed to find a solution that accounts for the space-time localization of radiation sources. Computational experiments were carried out and their results presented.
Keywords: radiative transfer equation, a Cauchy problem, Fresnel and diffuse matching conditions, Monte Carlo methods. 
@article{SEMR_2019_16_a94,
     author = {A. Kim and I. V. Prokhorov},
     title = {Initial-boundary value problem for a radiative transfer equation with generalized matching conditions},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1036--1056},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a94/}
}
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A. Kim; I. V. Prokhorov. Initial-boundary value problem for a radiative transfer equation with generalized matching conditions. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1036-1056. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a94/