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Sibirskii Zhurnal Industrial'noi Matematiki, 2020, Volume 23, Number 2, Pages 81–92
DOI: https://doi.org/10.33048/SIBJIM.2020.23.206 (Mi sjim1089) 		 
Reconstruction of the Lambert curve in a scattering medium by using pulsed sounding

V. A. Kanab, I. V. Prokhorovb

a Far-Eastern Federal University, ul. Sukhanova, Vladivostok 690950, Russia
b Institute for Applied Mathematics FEB RAS, ul. Radio, Vladivostok 690041, Russia
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DOI: https://doi.org/10.33048/SIBJIM.2020.23.206
Abstract: Under study is some mathematical model of the radiation transfer process in a scattering medium initiated by a pulsed point isotropic source. We inspect inverse problem of finding a diffusely reflecting curve by using the two integral overdetermination conditions on the solution of the radiative transfer equation. Some nonlinear differential equation is obtained for the function that describes the shape of the desired curve in the case of the single scattering approximation. Numerical analysis of the inverse problem solution is carried out to check the stability under perturbations of the initial data.
Keywords: inverse problem, radiation transfer equation, pulsed irradiation, diffuse reflection, volume scattering. .
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00173
Ministry of Science and Higher Education of the Russian Federation
German Academic Exchange Service (DAAD)
The authors were supported by the Russian Foundation for Basic Research (project no. 20-01-00173) and the Ministry of Education and Science of the Russian Federation and Deutscher Akademischer Austauschdienst (DAAD) according to the Program “Mikhail Lomonosov.”
Received: 27.01.2020
Revised: 27.01.2020
Accepted: 09.04.2020
English version:
Journal of Applied and Industrial Mathematics, 2020, Volume 14, Issue 2, Pages 321–329
DOI: https://doi.org/10.1134/S1990478920020106
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: V. A. Kan, I. V. Prokhorov, “Reconstruction of the Lambert curve in a scattering medium by using pulsed sounding”, Sib. Zh. Ind. Mat., 23:2 (2020), 81–92; J. Appl. Industr. Math., 14:2 (2020), 321–329
Citation in format AMSBIB
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\by V.~A.~Kan, I.~V.~Prokhorov
\paper Reconstruction of the Lambert curve in a scattering medium by using pulsed sounding
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 2
\pages 81--92
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\crossref{https://doi.org/10.33048/SIBJIM.2020.23.206}
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\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 2
\pages 321--329
\crossref{https://doi.org/10.1134/S1990478920020106}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85087682165}
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