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 Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 7, Pages 1226–1236 (Mi zvmmf627)

The maximum principle for the transport equation in the case of Compton scattering

D. S. Konovalova

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia

Abstract: The properties of solutions to the transport equation describing the Compton scattering of photons is investigated. The maximum and minimum principles are proved for this equation. According to them, the radiation density within a region cannot be greater than the maximum positive value of the incident radiation density and cannot be less than its minimum negative value. Furthermore, conditions under which a solution to the equation under consideration is constant are presented. The results of this work are obtained under the assumption that the properties of the medium change continuously with respect to the spatial and energy variables.

Key words: steady-state Compton scattering transport equation, maximum and minimum principles, mathematical modeling.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:7, 1185–1194

Bibliographic databases:
UDC: 519.634

Citation: D. S. Konovalova, “The maximum principle for the transport equation in the case of Compton scattering”, Zh. Vychisl. Mat. Mat. Fiz., 45:7 (2005), 1226–1236; Comput. Math. Math. Phys., 45:7 (2005), 1185–1194

Citation in format AMSBIB
\Bibitem{Kon05} \by D.~S.~Konovalova \paper The maximum principle for the transport equation in the case of Compton scattering \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2005 \vol 45 \issue 7 \pages 1226--1236 \mathnet{http://mi.mathnet.ru/zvmmf627} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2188414} \zmath{https://zbmath.org/?q=an:1116.78308} \transl \jour Comput. Math. Math. Phys. \yr 2005 \vol 45 \issue 7 \pages 1185--1194