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.
Citation:
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., 20:1 (2017), 75–85; J. Appl. Industr. Math., 11:1 (2017), 115–124
\Bibitem{ProSusKim17}
\by I.~V.~Prokhorov, A.~A.~Sushchenko, A.~Kim
\paper An initial boundary value problem for the radiative transfer equation with diffusion matching conditions
\jour Sib. Zh. Ind. Mat.
\yr 2017
\vol 20
\issue 1
\pages 75--85
\mathnet{http://mi.mathnet.ru/sjim950}
\crossref{https://doi.org/10.17377/sibjim.2017.20.108}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3629061}
\elib{https://elibrary.ru/item.asp?id=29044340}
\transl
\jour J. Appl. Industr. Math.
\yr 2017
\vol 11
\issue 1
\pages 115--124
\crossref{https://doi.org/10.1134/S1990478917010136}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85013988348}
Linking options:
https://www.mathnet.ru/eng/sjim950
https://www.mathnet.ru/eng/sjim/v20/i1/p75
This publication is cited in the following 22 articles:
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E. O. Kovalenko, I. V. Prokhorov, “Localization of the Discontinuity Lines of the Bottom Scattering Coefficient According to Acoustic Sounding Data”, J. Appl. Ind. Math., 16:1 (2022), 70
V. A. Kan, I. V. Prokhorov, “Reconstruction of the Lambert curve in a scattering medium by using pulsed sounding”, J. Appl. Industr. Math., 14:2 (2020), 321–329
I. V. Prokhorov, I. P. Yarovenko, “the Cauchy Problem For the Non-Stationary Radiative Transfer Equation With Compton Scattering”, Sib. Electron. Math. Rep., 17 (2020), 1943–1952
Yu. M. Timofeev, E. M. Shulgina, “Russian investigations in the field of atmospheric radiation in 2015-2018”, Izv. Atmos. Ocean. Phys., 56:1 (2020), 1–15
A. A. Amosov, “Boundary Value Problem for the Radiative Transfer Equation with Non-Lambert Diffuse Reflection and Diffuse Refraction Conditions”, J Math Sci, 247:6 (2020), 769
I. V. Prokhorov, “The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions”, Math. Notes, 105:1 (2019), 80–90
E. O. Kovalenko, I. V. Prokhorov, “Opredelenie koeffitsienta donnogo rasseyaniya pri mnogoluchevom zondirovanii okeana”, Dalnevost. matem. zhurn., 19:2 (2019), 206–222
I. V. Prokhorov, A. Kim, “Initial-Boundary Value Problem For a Radiative Transfer Equation With Generalized Matching Conditions”, Sib. Electron. Math. Rep., 16 (2019), 1036–1056
Andrei A. Sushchenko, Polina A. Vornovskikh, 2019 Days on Diffraction (DD), 2019, 196
I. V. Prokhorov, A. A. Suschenko, “Zadacha Koshi dlya uravneniya perenosa izlucheniya v neogranichennoi srede”, Dalnevost. matem. zhurn., 18:1 (2018), 101–111
V. A. Kan, I. V. Prokhorov, “Opredelenie diffuzno otrazhayuschei poverkhnosti pri impulsnom obluchenii”, Dalnevost. matem. zhurn., 18:2 (2018), 206–215
A. Kim, I. V. Prokhorov, “Theoretical and numerical analysis of an initial-boundary value problem for the radiative transfer equation with Fresnel matching conditions”, Comput. Math. Math. Phys., 58:5 (2018), 735–749
A. Amosov, “Nonstationary radiation transfer through a multilayered medium with reflection and refraction conditions”, Math. Meth. Appl. Sci., 41:17 (2018), 8115–8135
E. O. Kovalenko, A. A. Sushchenko, V. A. Kan, “Focusing of sonar images as an inverse problem for radiative transfer equation”, 24Th International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics, Proceedings of SPIE, 10833, eds. G. Matvienko, O. Romanovskii, Spie-Int Soc Optical Engineering, 2018, UNSP 108336D
A. A. Amosov, “Initial-Boundary Value Problem for the Non-Stationary Radiative Transfer Equation with Fresnel Reflection and Refraction Conditions”, J Math Sci, 231:3 (2018), 279
A. A. Amosov, “Initial-Boundary Value Problem for the Nonstationary Radiative Transfer Equation with Diffuse Reflection and Refraction Conditions”, J Math Sci, 235:2 (2018), 117
A. Kim, I. V. Prokhorov, 2017 Days on Diffraction (DD), 2017, 168
V. A. Kan, I. V. Prokhorov, A. A. Sushchenko, 2017 Days on Diffraction (DD), 2017, 163
Elisaveta Lyu, Andrei Sushchenko, Igor Prokhorov, Vladimir Kan, Oleg A. Romanovskii, 23rd International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics, 2017, 271
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