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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.

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Authors and Affiliations

  1. Institute for Applied Mathematics, Far-Eastern Branch, Russian Academy of Sciences, Vladivostok, 690041, Russia

    I. V. Prokhorov

  2. Far-Eastern Federal University, Vladivostok, 690950, Russia

    I. V. Prokhorov

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  1. I. V. Prokhorov
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Correspondence to I. V. Prokhorov.

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Russian Text © I. V. Prokhorov, 2019, published in Matematicheskie Zametki, 2019, Vol. 105, No. 1, pp. 95–107.

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Prokhorov, I.V. The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions. Math Notes 105, 80–90 (2019). https://doi.org/10.1134/S0001434619010097

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  • DOI: https://doi.org/10.1134/S0001434619010097

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