# The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions

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## Abstract

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## Preview

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