This article is cited in 22 papers

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

I. V. Prokhorov^ab, A. A. Sushchenko<sup>ba

a</sup> 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.

UDC: 517.958

Received: 02.06.2014

DOI: 10.17377/smzh.2015.56.415

 English version: Siberian Mathematical Journal, 2015, 56:4, 736–745

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