Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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 6 scientific papers (total in 6 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 (6)
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
\Bibitem{ProYar21}
\by I.~V.~Prokhorov, I.~P.~Yarovenko
\paper Determination of the attenuation coefficient for the nonstationary radiative transfer equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2021
\vol 61
\issue 12
\pages 2095--2108
\mathnet{http://mi.mathnet.ru/zvmmf11334}
\crossref{https://doi.org/10.31857/S0044466921120115}
\elib{https://elibrary.ru/item.asp?id=46713032}
\transl
\jour Comput. Math. Math. Phys.
\yr 2021
\vol 61
\issue 12
\pages 2088--2101
\crossref{https://doi.org/10.1134/S0965542521120101}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000742039500013}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85122726630}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf11334
  • https://www.mathnet.ru/eng/zvmmf/v61/i12/p2095
    • This publication is cited in the following 6 articles:
    1. M. A. Donskaya, I. P. Yarovenko, “O vybore metoda rozygrysha svobodnogo probega pri reshenii nestatsionarnogo uravneniya perenosa izlucheniya s ispolzovaniem graficheskikh uskoritelei”, Dalnevost. matem. zhurn., 24:1 (2024), 33–44  mathnet  crossref
    2. I. P. Yarovenko, P. A. Vornovskikh, I. V. Prokhorov, “Extrapolation of tomographic images based on data of multiple pulsed probing”, J. Appl. Industr. Math., 18:3 (2024), 583–597  mathnet  crossref  crossref
    3. Vasily G. Nazarov, Igor V. Prokhorov, Ivan P. Yarovenko, “Identification of an Unknown Substance by the Methods of Multi-Energy Pulse X-ray Tomography”, Mathematics, 11:15 (2023), 3263  crossref
    4. Ivan P. Yarovenko, Igor V. Prokhorov, “An extrapolation method for improving the quality of tomographic images using multiple short-pulse irradiations”, Journal of Inverse and Ill-posed Problems, 2023  crossref
    5. P. A. Vornovskikh, E. V. Ermolaev, I. V. Prokhorov, “On the problem of determining the scattering coefficient in frequency modulated sounding of a medium”, Dalnevost. matem. zhurn., 22:2 (2022), 263–268  mathnet  crossref  mathscinet
    6. I. P. Yarovenko, I. G. Kazantsev, “An extrapolation method for improving the linearity of CT-values in X-ray pulsed tomography”, Dalnevost. matem. zhurn., 22:2 (2022), 269–275  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Statistics & downloads:
    Abstract page:332
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025