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Mat. Zametki, 2019, Volume 105, Issue 1, Pages 95–107 (Mi mz11844)  

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

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.

Funding Agency Grant Number
Russian Science Foundation 14-11-00079
This work was supported by the Russian Science Foundation under grant 14-11-00079.


DOI: https://doi.org/10.4213/mzm11844

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English version:
Mathematical Notes, 2019, 105:1, 80–90

Bibliographic databases:

Document Type: Article
UDC: 517.958
PACS: 42.25.Dd
Received: 31.10.2017
Revised: 07.02.2018

Citation: I. V. Prokhorov, “The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions”, Mat. Zametki, 105:1 (2019), 95–107; Math. Notes, 105:1 (2019), 80–90

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