This article is cited in 8 papers

The Cauchy problem for the radiatve transfer equation in an unbounded medium

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

a</sup> Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
^b Far Eastern Federal University, Vladivostok

Abstract: The correctness of the Cauchy problem of the integro-differential radiation transfer equation in a system of two unbounded subdomains, separated by a reflecting and refracting surface, is investigated. The existence of a unique strongly continuous semigroup of resolving operators of the Cauchy problem is proved. Conditions on the order of growth of the semigroup are obtained.

Key words: radiative transfer equation, Cauchy problem, generalized matching conditions.

UDC: 517.958

MSC: Primary 35Q20; Secondary 35Q60

Received: 16.03.2018