The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions
I. V. Prokhorovab
a Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
b Far Eastern Federal University, Vladivostok
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.
radiation transfer equation, initial boundary-value problem, matching conditions, Fresnel's and Lambert's laws.
|Russian Science Foundation
|This work was supported
by the Russian Science Foundation
under grant 14-11-00079.
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I. V. Prokhorov, “The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions”, Mat. Zametki, 105:1 (2019), 95–107
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\paper The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions
\jour Mat. Zametki
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