Geodesic
The Cauchy problem for the non-stationary radiative transfer equation with Compton scattering
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1943-1952

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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. 
@article{SEMR_2020_17_a106,
     author = {I. V. Prokhorov and I. P. Yarovenko},
     title = {The {Cauchy} problem for the non-stationary radiative transfer equation with {Compton} scattering},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1943--1952},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a106/}
}
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I. V. Prokhorov; I. P. Yarovenko. The Cauchy problem for the non-stationary radiative transfer equation with Compton scattering. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1943-1952. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a106/