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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
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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