I. V. Prokhorov, “On the Structure of the Continuity Set of the Solution to a Boundary-Value Problem for the Radiation Transfer Equation”, Mat. Zametki, 86:2 (2009), 256–272; Math. Notes, 86:2 (2009), 234

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Matematicheskie Zametki, 2009, Volume 86, Issue 2, Pages 256–272
DOI: https://doi.org/10.4213/mzm4149 (Mi mzm4149)

This article is cited in 16 scientific papers (total in 16 papers)

On the Structure of the Continuity Set of the Solution to a Boundary-Value Problem for the Radiation Transfer Equation

I. V. Prokhorov

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences

Full-text PDF (545 kB) Citations (16)

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DOI: https://doi.org/10.4213/mzm4149

Abstract: In this paper, we study the continuity properties of the solution to a boundary-value problem for the radiation transfer equation with generalized conjugation conditions at the interface of media. We establish the solvability of the boundary-value problem and obtain estimates of the maximum principle type. It is shown that the Fresnel component in the conjugation operator significantly complicates the structure of the set on which the solution of the boundary-value problem is continuous.

Keywords: radiation transfer equation, boundary-value problem, conjugation operator, Fresnel reflection, diffuse reflection, reflection indicatrix, Snell's law, index of refraction.

Received: 26.03.2007
Revised: 17.06.2008

English version:
Mathematical Notes, 2009, Volume 86, Issue 2, Pages 234–248
DOI: https://doi.org/10.1134/S0001434609070256

Bibliographic databases:

UDC: 517.958

Language: Russian

Citation: I. V. Prokhorov, “On the Structure of the Continuity Set of the Solution to a Boundary-Value Problem for the Radiation Transfer Equation”, Mat. Zametki, 86:2 (2009), 256–272; Math. Notes, 86:2 (2009), 234–248

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Linking options:

https://www.mathnet.ru/eng/mzm4149

https://doi.org/10.4213/mzm4149

https://www.mathnet.ru/eng/mzm/v86/i2/p256

This publication is cited in the following 16 articles:

Chebotarev A.Yu., Kovtanyuk A.E., “Quasi-Static Diffusion Model of Complex Heat Transfer With Reflection and Refraction Conditions”, J. Math. Anal. Appl., 507:1 (2022), 125745
I. V. Prokhorov, “The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions”, Math. Notes, 105:1 (2019), 80–90
A. Kim, I. V. Prokhorov, “Initial-boundary value problem for a radiative transfer equation with generalized matching conditions”, Sib. elektron. matem. izv., 16 (2019), 1036–1056
Yarovenko I.P., Prokhorov I.V., “Determination of Refractive Indices of a Layered Medium Under Pulsed Irradiation”, Opt. Spectrosc., 124:4 (2018), 567–574
I. V. Prokhorov, A. A. Suschenko, “Zadacha Koshi dlya uravneniya perenosa izlucheniya v neogranichennoi srede”, Dalnevost. matem. zhurn., 18:1 (2018), 101–111
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
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
Vornovskikh P.A., Sushchenko A.A., “Remote Sensing Problem With Multiple Scattering Effect”, 23Rd International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics, Proceedings of Spie, 10466, no. 1, eds. Matvienko G., Romanovskii O., Spie-Int Soc Optical Engineering, 2017, UNSP 104661Y
Filimonov M., Vaganova N., “Permafrost Thawing From Different Technical Systems in Arctic Regions”, International Conference on Sustainable Cities, IOP Conf. Ser. Earth Envir. Sci., IOP Conference Series-Earth and Environmental Science, 72, IOP Publishing Ltd, 2017, UNSP 012006
A. A. Amosov, “Radiative Transfer Equation with Fresnel Reflection and Refraction Conditions in a System of Bodies with Piecewise Smooth Boundaries”, J Math Sci, 219:6 (2016), 821
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
I.V. Prokhorov, A.A. Sushchenko, “Imaging Based on Signal from Side-Scan Sonar”, AMM, 756 (2015), 678
I. V. Prokhorov, “The Cauchy problem for the radiative transfer equation with generalized conjugation conditions”, Comput. Math. Math. Phys., 53:5 (2013), 588–600
Timofeev Yu.M., Shul'gina E.M., “Russian Investigations in the Field of Atmospheric Radiation in 2007-2010”, Izv. Atmos. Ocean. Phys., 49:1 (2013), 16–32
I. V. Prokhorov, “Solvability of the initial-boundary value problem for an integrodifferential equation”, Siberian Math. J., 53:2 (2012), 301–309
I. V. Prokhorov, V. V. Zolotarev, I. B. Agafonov, “Zadacha akusticheskogo zondirovaniya vo fluktuiruyuschem okeane”, Dalnevost. matem. zhurn., 11:1 (2011), 76–87

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

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