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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 5, Pages 753–766 (Mi zvmmf9856)  

This article is cited in 12 scientific papers (total in 12 papers)

The Cauchy problem for the radiative transfer equation with generalized conjugation conditions

I. V. Prokhorovab

a Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok
b Far Eastern Federal University, Vladivostok

Abstract: The initial boundary problem for the nonstationary radiative transfer equation in a nonhomogeneous plane layer with generalized conjugation conditions on the material interface is studied. A generalized Monte-Carlo algorithm is proposed for solving the problem, and numerical experiments are discussed.

Key words: nonstationary transfer equation, generalized conjugation conditions, Monte-Carlo method.

DOI: https://doi.org/10.7868/S004446691305013X

Full text: PDF file (693 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:5, 588–600

Bibliographic databases:

UDC: 519.634
Received: 24.05.2012
Revised: 06.12.2012

Citation: I. V. Prokhorov, “The Cauchy problem for the radiative transfer equation with generalized conjugation conditions”, Zh. Vychisl. Mat. Mat. Fiz., 53:5 (2013), 753–766; Comput. Math. Math. Phys., 53:5 (2013), 588–600

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. V. Prokhorov, A. S. Zhuplev, “Ob effektivnosti metodov maksimalnogo secheniya v teorii perenosa izlucheniya”, Kompyuternye issledovaniya i modelirovanie, 5:4 (2013), 573–582  elib
    2. I. V. Prokhorov, A. A. Sushchenko, “On the well-posedness of the Cauchy problem for the equation of radiative transfer with Fresnel matching conditions”, Siberian Math. J., 56:4 (2015), 736–745  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. A. Kim, I. V. Prokhorov, “Monte Carlo method for non-stationary radiative transfer equation in inhomogeneous media”, XXII International Symposium Atmospheric and Ocean Optics. Atmospheric Physics (Tomsk, Russian Federation, Thursday 30 June 2016), SPIE Proceedings, 10035, eds. G. Matvienko, O. Romanovskii, Spie-Int Soc Optical Engineering, 2016, 100350Z  crossref  isi  scopus
    4. A. A. Astrakhantseva, A. Yu. Chebotarev, G. V. Grenkin, A. E. Kovtanyuk, “Numerical analysis of the complex heat transfer in a layered medium”, 2016 Days on Diffraction (DD) (St.Petersburg, Russia), eds. O. Motygin, A. Kiselev, P. Kapitanova, L. Goray, A. Kazakov, A. Kirpichnikova, IEEE, 2016, 21–24  crossref  isi  scopus
    5. A. Yu. Chebotarev, G. V. Grenkin, A. E. Kovtanyuk, I. V. Prokhorov, “Analysis of a diffraction problem for equations of complex heat transfer”, 2016 Days on Diffraction (DD) (St.Petersburg, Russia), eds. O. Motygin, A. Kiselev, P. Kapitanova, L. Goray, A. Kazakov, A. Kirpichnikova, IEEE, 2016, 101–105  crossref  isi  scopus
    6. A. Amosov, M. Shumarov, “Boundary value problem for radiation transfer equation in multilayered medium with reflection and refraction conditions”, Appl. Anal., 95:7, SI (2016), 1581–1597  crossref  mathscinet  zmath  isi  elib  scopus
    7. I. V. Prokhorov, A. A. Sushchenko, A. Kim, “An initial boundary value problem for the radiative transfer equation with diffusion matching conditions”, J. Appl. Industr. Math., 11:1 (2017), 115–124  mathnet  crossref  crossref  mathscinet  elib
    8. P. A. Vornovskikh, A. A. Sushchenko, “Remote sensing problem with multiple scattering effect”, 23rd International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics, Proceedings of SPIE, 10466, eds. G. Matvienko, O. Romanovskii, SPIE-Int. Soc. Optical Engineering, 2017, UNSP 104661Y  crossref  isi  scopus
    9. I. P. Yarovenko, I. V. Prokhorov, “Determination of refractive indices of a layered medium under pulsed irradiation”, Opt. Spectrosc., 124:4 (2018), 567–574  crossref  isi  scopus
    10. I. V. Prokhorov, A. A. Suschenko, “Zadacha Koshi dlya uravneniya perenosa izlucheniya v neogranichennoi srede”, Dalnevost. matem. zhurn., 18:1 (2018), 101–111  mathnet
    11. 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  mathnet  crossref  crossref  isi  elib
    12. I. V. Prokhorov, “The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions”, Math. Notes, 105:1 (2019), 80–90  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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