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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 12, Pages 2095–2108
DOI: https://doi.org/10.31857/S0044466921120115 (Mi zvmmf11334) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Mathematical physics

Determination of the attenuation coefficient for the nonstationary radiative transfer equation

I. V. Prokhorovab, I. P. Yarovenkoa

a Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, 690041, Vladivostok, Russia
b Far Eastern Federal University, 690950, Vladivostok, Russia
Citations (5)
DOI: https://doi.org/10.31857/S0044466921120115
Abstract: For the nonstationary radiative transfer equation, the inverse problem of determining the attenuation coefficient from a known solution at the domain boundary is considered. The structure and the continuous properties of the solution to an initial-boundary value problem for the radiative transfer equation are studied. Under special assumptions about the radiation source, it is shown that the inverse problem has a unique solution and a formula for the Radon transform of the attenuation coefficient is derived. The quality of the reconstructed tomographic images of the sought function is analyzed numerically in the case of various angular and time flux density distributions of the external source.
Key words: nonstationary radiative transfer equation, radiation sources, inverse problems, attenuation coefficient, tomography.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00173
Ministry of Education and Science of the Russian Federation 075-01095-20-00
075-02-2020-1482-1
This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00173) and by the Ministry of Science and Higher Education of the Russian Federation (agreement nos. 075-01095-20-00, 075-02-2020-1482-1).
Received: 28.03.2020
Revised: 28.06.2021
Accepted: 04.08.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 12, Pages 2088–2101
DOI: https://doi.org/10.1134/S0965542521120101
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: I. V. Prokhorov, I. P. Yarovenko, “Determination of the attenuation coefficient for the nonstationary radiative transfer equation”, Zh. Vychisl. Mat. Mat. Fiz., 61:12 (2021), 2095–2108; Comput. Math. Math. Phys., 61:12 (2021), 2088–2101
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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