Differentical equations, dynamical systems and optimal control

The Cauchy problem for the non-stationary radiative transfer equation with Compton scattering

I. V. Prokhorov^ab, I. P. Yarovenko<sup>a

a</sup> Institute of Applied Mathematics FEB RAS, 7, Radio str., Vladivostok, 690041, Russia
^b Far Eastern Federal University, 8, Sukhanova str. , Vladivostok, 690950, Russia

Abstract: The paper considers the initial-boundary-value problem for the radiative transfer equation in an inhomogeneous medium with a collision integral that describes Compton scattering by free electrons. The problem is reduced to abstract Cauchy problem in Banach space. Using the theory of strongly continuous semigroups, well-posedness of the Cauchy problem is proved. Conditions of the operator semigroup stability are found.

Keywords: radiative transfer equation, Compton scattering, Cauchy problem, strongly continuous semigroup.

UDC: 517.958

MSC: 35Q20, 35Q60

Received June 23, 2020, published November 26, 2020

DOI: 10.33048/semi.2020.17.130

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