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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 1943–1952
DOI: https://doi.org/10.33048/semi.2020.17.130 (Mi semr1324) 		 
Differentical equations, dynamical systems and optimal control

The Cauchy problem for the non-stationary radiative transfer equation with Compton scattering

I. V. Prokhorovab, I. P. Yarovenkoa

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.2020.17.130
Abstract: The paper considers the initial-boundary-value problem for the radiative transfer equation in an inhomogeneous medium with a collision integral that describes Compton scattering by free electrons. The problem is reduced to abstract Cauchy problem in Banach space. Using the theory of strongly continuous semigroups, well-posedness of the Cauchy problem is proved. Conditions of the operator semigroup stability are found.
Keywords: radiative transfer equation, Compton scattering, Cauchy problem, strongly continuous semigroup.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00173
Received June 23, 2020, published November 26, 2020
Bibliographic databases:
Document Type: Article
UDC: 517.958
MSC: 35Q20, 35Q60
Language: Russian
Citation: I. V. Prokhorov, I. P. Yarovenko, “The Cauchy problem for the non-stationary radiative transfer equation with Compton scattering”, Sib. Èlektron. Mat. Izv., 17 (2020), 1943–1952
Citation in format AMSBIB
\Bibitem{ProYar20}
\by I.~V.~Prokhorov, I.~P.~Yarovenko
\paper The Cauchy problem for the non-stationary radiative transfer equation with Compton scattering
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 1943--1952
\mathnet{http://mi.mathnet.ru/semr1324}
\crossref{https://doi.org/10.33048/semi.2020.17.130}
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