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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2019, Volume 16, Pages 1036–1056
DOI: https://doi.org/10.33048/semi.2019.16.072 (Mi semr1113) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Differentical equations, dynamical systems and optimal control

Initial-boundary value problem for a radiative transfer equation with generalized matching conditions

A. Kimab, I. V. Prokhorovab

a Institute of Applied Mathematics FEB RAS, 7, Radio str., Vladivostok, 690041, Russia
b Far Eastern Federal University 8, Sukhanova str., Vladivostok, 690950, Russia
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DOI: https://doi.org/10.33048/semi.2019.16.072
Abstract: We consider the Cauchy problem for a non-stationary radiative transfer equation in a three-dimensional multicomponent medium with generalized matching conditions. These matching condition describe Fresnel and diffuse reflection and refraction at the interfaces. The existence and uniqueness of a solution of the initial-boundary value problem is proved. We construct a Monte-Carlo numerical method designed to find a solution that accounts for the space-time localization of radiation sources. Computational experiments were carried out and their results presented.
Keywords: radiative transfer equation, a Cauchy problem, Fresnel and diffuse matching conditions, Monte Carlo methods.
Received April 22, 2019, published August 7, 2019
Bibliographic databases:
Document Type: Article
UDC: 517.958
MSC: 35Q20 + 35Q60
Language: English
Citation: A. Kim, I. V. Prokhorov, “Initial-boundary value problem for a radiative transfer equation with generalized matching conditions”, Sib. Èlektron. Mat. Izv., 16 (2019), 1036–1056
Citation in format AMSBIB
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\by A.~Kim, I.~V.~Prokhorov
\paper Initial-boundary value problem for a radiative transfer equation with generalized matching conditions
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1036--1056
\mathnet{http://mi.mathnet.ru/semr1113}
\crossref{https://doi.org/10.33048/semi.2019.16.072}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000479063900005}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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