Geodesic
Method of solution of the radiation transfer equation for an optically thick layer with reflecting boundaries
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 2, pp. 287-302 
V. S. Potapov. Method of solution of the radiation transfer equation for an optically thick layer with reflecting boundaries. Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 2, pp. 287-302. http://geodesic.mathdoc.fr/item/TMF_1994_100_2_a10/
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     author = {V. S. Potapov},
     title = {Method of solution of the radiation transfer equation for an optically thick layer with reflecting boundaries},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {287--302},
     year = {1994},
     volume = {100},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_100_2_a10/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A method is developed for solving the equations of the theory of radiative transfer that is effective for an optically thick reflecting layer. The essence of the method is to go over in the transfer equation to Laplace transforms and then investigate their analytic properties and eliminate fictitious singularities. Relations are formulated for the boundary values of the intesities; in conjunction with the boundary conditions these form a closed system of linear integral Fredholm equations of the second kind with completely continuous kernels.

[1] Chandrasekar S., Perenos luchistoi energii, Inostr. lit., M., 1953

[2] Devison B., Teoriya perenosa neitronov, Atomizdat, M., 1960

[3] Marnuk G. I., Lebedev V. I., Chislennye metody v teorii perenosa neitronov, Nauka, M., 1981 | MR

[4] Germogenova T. A., Lokalnye svoistva reshenii uravneniya perenosa, Nauka, M., 1986 | MR | Zbl

[5] Sobolev V. V., Perenos luchistoi energii v atmosferakh zvezd i planet, GITTL, M., 1956 | MR

[6] Busbridge I. W., Ap. J., 122:2 (1960), 1955 | MR

[7] Mullikin T. W., Astrophys. J., 139 (1964), 379, 1267 ; Carlsted J. L., Mullikin T. W., Astrophys. J. Suppl. ser., 12:113 (1966) | DOI

[8] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968 | MR | Zbl