I. V. Prokhorov, A. A. Sushchenko, A. Kim, “An initial boundary value problem for the radiative transfer equation with diffusion matching conditions”, Sib. Zh. Ind. Mat., 2017, Volume 20, Number 1,Pages <nobr>75

This article is cited in 22 papers

An initial boundary value problem for the radiative transfer equation with diffusion matching conditions

I. V. Prokhorov^ab, A. A. Sushchenko^ab, A. Kim^b

^a Institute of Applied Mathematics Far Eastern Branch RAS, Radio str., 7, 690041 Vladivostok
^b Far Eastern Federal University, Sukhanov str., 8, 690950 Vladivostok

Abstract: We consider the Cauchy problem for the nonstationary equation of radiative transfer with generalized matching conditions describing the diffusion reflection and refraction on the separation boundary of the media. We prove solvability of the initial boundary value problem and obtainh stabilization conditions for an unsteady solution.

Keywords: diffusion matching conditions, integro-differential equation, nonstationary equation, Cauchy problem, Hille–Yosida theorem.

UDC: 517.958

Received: 14.01.2016

DOI: 10.17377/sibjim.2017.20.108