Sobolev's ?-function of radiative transfer in planar and spherical scattering media

Autor:	S. Ueno, P. T. Y. Poon
Rok vydání:	1974
Předmět:	Cauchy problem Physics Sobolev space Classical mechanics Laplace transform Space and Planetary Science Mathematical analysis Radiative transfer Cauchy distribution Astronomy and Astrophysics Integral equation Sobolev spaces for planar domains Resolvent
Zdroj:	Astrophysics and Space Science. 28:233-244
ISSN:	1572-946X 0004-640X
DOI:	10.1007/bf00642253
Popis:	In recent years Sobolev's Φ-function of radiative transfer has been discussed in connection with the resolvent of Milne's integral equation such that it plays an important role in the determination of the radiation field in semi-infinite (or finite) atmospheres with internal sources (cf. Sobolev, 1963). In the present paper, the part of Sobolev's Φ-function in plane-parallel and spherical, isotropically scattering, atmospheres with internal source distribution is investigated from analytical and numerical aspects. With the aid of invariant imbedding (cf. Bellmanet al., 1968), we computed Sobolev's Φ-function of Milne's integral equation for the planar case by solving the Cauchy system for the auxiliary function and Chandrasekhar'sX- andY-functions. The corresponding Φ-function for the spherical case is readily obtained from the for the planar case.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::2d3a0db7ecbd4c423314f769413f17fb https://doi.org/10.1007/bf00642253 Zobrazit plný text záznamu Full text from SpringerLink