Geodesic
The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions
Matematičeskie zametki, Tome 105 (2019) no. 1, pp. 95-107

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The well-posedness of the initial boundary-value problem for the nonstationary radiation transfer equation in a three-dimensional bounded domain with generalized matching conditions at the interfaces is studied. The case of the matching operator expressed as a linear combination of operators of Fresnel and Lambert types is considered. The existence of a unique strongly continuous semigroup of solving operators of the Cauchy problem is proved, and stabilization conditions for the nonstationary solution are obtained.
Keywords: radiation transfer equation, initial boundary-value problem, matching conditions, Fresnel's and Lambert's laws. 
I. V. Prokhorov. The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions. Matematičeskie zametki, Tome 105 (2019) no. 1, pp. 95-107. http://geodesic.mathdoc.fr/item/MZM_2019_105_1_a8/
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     title = {The {Cauchy} {Problem} for the {Radiation} {Transfer} {Equation} with {Fresnel} and {Lambert} {Matching} {Conditions}},
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