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Dal'nevost. Mat. Zh., 2018, Volume 18, Number 1, Pages 101–111 (Mi dvmg371)  

This article is cited in 1 scientific paper (total in 1 paper)

The Cauchy problem for the radiatve transfer equation in an unbounded medium

I. V. Prokhorovab, A. A. Sushchenkoab

a Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
b Far Eastern Federal University, Vladivostok

Abstract: The correctness of the Cauchy problem of the integro-differential radiation transfer equation in a system of two unbounded subdomains, separated by a reflecting and refracting surface, is investigated. The existence of a unique strongly continuous semigroup of resolving operators of the Cauchy problem is proved. Conditions on the order of growth of the semigroup are obtained.

Key words: radiative transfer equation, Cauchy problem, generalized matching conditions.

Funding Agency Grant Number
ПФИ ДВО РАН “Дальний Восток” 18-5-050
Russian Foundation for Basic Research 18-31-00050


Full text: PDF file (263 kB)
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Document Type: Article
UDC: 517.958
MSC: Primary 35Q20; Secondary 35Q60
Received: 16.03.2018

Citation: I. V. Prokhorov, A. A. Sushchenko, “The Cauchy problem for the radiatve transfer equation in an unbounded medium”, Dal'nevost. Mat. Zh., 18:1 (2018), 101–111

Citation in format AMSBIB
\Bibitem{ProSus18}
\by I.~V.~Prokhorov, A.~A.~Sushchenko
\paper The Cauchy problem for the radiatve transfer equation in an unbounded medium
\jour Dal'nevost. Mat. Zh.
\yr 2018
\vol 18
\issue 1
\pages 101--111
\mathnet{http://mi.mathnet.ru/dvmg371}


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    This publication is cited in the following articles:
    1. V. A. Kan, I. V. Prokhorov, “Opredelenie diffuzno otrazhayuschei poverkhnosti pri impulsnom obluchenii”, Dalnevost. matem. zhurn., 18:2 (2018), 206–215  mathnet
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