Geodesic
Unique solvability of boundary value problem for a polychromatic radiation transfer equation
Dalʹnevostočnyj matematičeskij žurnal, Tome 19 (2019) no. 1, pp. 96-107.

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The paper deals with a boundary value problem for a radiation transfer equation. It's assumed that Compton scattering is predominant effect in media. The boundary value problem is reduced to an integral equation of Volterra type. The result of the work is the theorem provides existence and uniqueness of solution for the boundary value problem of the radiative transfer equation. 
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I. P. Yarovenko. Unique solvability of boundary value problem for a polychromatic radiation transfer equation. Dalʹnevostočnyj matematičeskij žurnal, Tome 19 (2019) no. 1, pp. 96-107. http://geodesic.mathdoc.fr/item/DVMG_2019_19_1_a11/

[1] D. S. Anikonov, D. S. Konovalova, “Kineticheskoe uravnenie perenosa dlya sluchaya komptonovskogo rasseyaniya”, Sibirskii matematicheskii zhurnal, 43:5 (2002), 987–1001 | MR | Zbl

[2] D. S. Anikonov, D. S. Konovalova, “Kraevaya zadacha dlya uravneniya perenosa s chisto komptonovskim rasseyaniem”, Sibirskii matematicheskii zhurnal, 46:1 (2005), 3–16 | MR | Zbl

[3] I. P. Yarovenko, “O razreshimosti kraevoi zadachi dlya uravneniya perenosa izlucheniya s uchetom komptonovskogo rasseyaniya”, Dalnevost. matem. zhurn., 14:1 (2014), 109–121 | MR | Zbl

[4] A. V. Chernov, “Ob odnom mazhorantno-minorantnom priznake totalnogo sokhraneniya globalnoi razreshimosti upravlyaemykh raspredelennykh sistem”, Differentsialnye uravneniya, 52:1 (2016), 112 | DOI | MR | Zbl

[5] V. S. Vladimirov, Matematicheskie zadachi odnoskorostnoi teorii perenosa chastits, Tr. MIAN SSSR, Izd-vo AN SSSR, M., 1961, 61 pp.

[6] T. A. Germogenova, “Obobschennye resheniya kraevykh zadach dlya uravneniya perenosa”, Zh. vychisl. matem. i matem. fiz., 9:3 (1969), 605–-625 | MR | Zbl

[7] V. I. Agoshkov, Obobschennye resheniya uravneniya perenosa i svoistva ikh gladkosti, Nauka, M., 1988

[8] V. A. Zorich, Matematicheskii analiz, Nauka, M., 1984

[9] A. A. Amosov, Kraevye zadachi dlya uravneniya perenosa izlucheniya s usloviyami otrazheniya i prelomleniya, Tamara Rozhkovskaya, Novosibirsk., 2017

[10] S. M. Nikolskii, Kurs matematicheskogo analiza, Nauka, M., 1975

[11] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Fizmatlit, M., 2004