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 Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 1036–1056 (Mi semr1113)

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

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.

DOI: https://doi.org/10.33048/semi.2019.16.072

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Bibliographic databases:

UDC: 517.958
MSC: 35Q20 + 35Q60
Received April 22, 2019, published August 7, 2019
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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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