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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
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
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
Linking options:
https://www.mathnet.ru/eng/smj2687 https://www.mathnet.ru/eng/smj/v56/i4/p922
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Abstract page: | 878 | Full-text PDF : | 78 | References: | 99 | First page: | 7 |
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