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Matematicheskie Zametki, 2019, Volume 105, Issue 1, Pages 95–107
DOI: https://doi.org/10.4213/mzm11844 (Mi mzm11844) 		 
This article is cited in 10 scientific papers (total in 10 papers)

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
Full-text PDF (518 kB) Citations (10)
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DOI: https://doi.org/10.4213/mzm11844
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.
Received: 31.10.2017
Revised: 07.02.2018
English version:
Mathematical Notes, 2019, Volume 105, Issue 1, Pages 80–90
DOI: https://doi.org/10.1134/S0001434619010097
Bibliographic databases:
Document Type: Article
UDC: 517.958
PACS: 42.25.Dd
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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