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. 
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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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