Far Eastern Mathematical Journal

To content of the issue


Unique solvability of boundary value problem for a polychromatic radiation transfer equation


Yarovenko I.P.

2019, issue 1, Ñ. 96-107


Abstract
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.

Keywords:
radiation transfer theory, Compton scattering

Download the article (PDF-file)

References

[1] D.S. Anikonov, D.S. Konovalova, “Kineticheskoe uravnenie perenosa dlia sluchaia komptonovskogo rasseianiia”, Sibirskii matematicheskii zhurnal, 43:5, (2002), 987–1001.
[2] D.S. Anikonov, D.S. Konovalova, “Kraevaia zadacha dlia uravneniia perenosa s chisto komptonovskim rasseianiem”, Sibirskii matematicheskii zhurnal, 46:1, (2005), 3–16.
[3] I.P. Iarovenko, “O razreshimosti kraevoi zadachi dlia uravneniia perenosa izlucheniia s uchetom komptonovskogo rasseianiia”, Dal'nevost. matem. zhurn., 14:1, (2014), 109–121.
[4] A.V. Chernov, “Ob odnom mazhorantno-minorantnom priznake total'nogo sokhraneniia global'noi razreshimosti upravliaemykh raspredelennykh sistem”, Differentsial'nye uravneniia, 52:1, (2016), 112.
[5] V.S. Vladimirov, Matematicheskie zadachi odnoskorostnoi teorii perenosa chastits, Tr. MIAN SSSR, Izd-vo AN SSSR, M., 1961, 61 s.
[6] T.A. Germogenova, “Obobshchennye resheniia kraevykh zadach dlia uravneniia perenosa”, Zh. vychisl. matem. i matem. fiz., 9:3, (1969), 605–625.
[7] V.I. Agoshkov, Obobshchennye resheniia uravneniia perenosa i svoistva ikh gladkosti, Nauka, M., 1988.
[8] V.A. Zorich, Matematicheskii analiz, Nauka, M., 1984.
[9] A.A. Amosov, Kraevye zadachi dlia uravneniia perenosa izlucheniia s usloviiami otrazheniia i prelomleniia, Tamara Rozhkovskaia, Novosibirsk, 2017.
[10] S.M. Nikol'skii, Kurs matematicheskogo analiza, Nauka, M., 1975.
[11] A.N. Kolmogorov, S.V. Fomin, Elementy teorii funktsii i funktsional'nogo analiza, Fizmatlit, M., 2004.

To content of the issue