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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 4, Pages 922–933
DOI: https://doi.org/10.17377/smzh.2015.56.415 (Mi smj2687) 		 
This article is cited in 22 scientific papers (total in 22 papers)

On the well-posedness of the Cauchy problem for the equation of radiative transfer with Fresnel matching conditions

I. V. Prokhorovab, A. A. Sushchenkoba

a Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok, Russia
b Far Eastern Federal University, Vladivostok, Russia
Full-text PDF (309 kB) Citations (22)
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DOI: https://doi.org/10.17377/smzh.2015.56.415
Abstract: We study the well-posedness of the Cauchy problem for the nonstationary equation of radiative transfer in a three-dimensional bounded domain with Fresnel matching conditions on the interfaces. We prove the existence of a unique strongly continuous semigroup of resolvent operators, and obtain stabilization conditions for nonstationary solutions.
Keywords: integrodifferential equations, nonstationary equations, Cauchy problem, Fresnel matching conditions, Hille–Yosida theorem.
Received: 02.06.2014
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 4, Pages 736–745
DOI: https://doi.org/10.1134/S0037446615040151
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: I. V. Prokhorov, A. A. Sushchenko, “On the well-posedness of the Cauchy problem for the equation of radiative transfer with Fresnel matching conditions”, Sibirsk. Mat. Zh., 56:4 (2015), 922–933; Siberian Math. J., 56:4 (2015), 736–745
Citation in format AMSBIB
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    • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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