Exact solution of the equation of transfer in a finite exponential atmosphere by the method of laplace transform and linear singular operators
Abstract
The equation which commonly appears in radiative transfer problem in a finite atmosphere having ground reflection according to Lambert's law is considered in this paper. The Planck's functionB _{ν}(T) is taken in the form, <MediaObject> <ImageObject FileRef="10509_2004_Article_BF00639094_TeX2GIFE1.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"/> </MediaObject> B_v (T) = b_0 + b_1 e^{  β tau } . The exact solution of this equation is obtained for surface quantities in terms of theXY equations of Chandrasekhar by the method of Laplace transform and linear singular operators.
 Publication:

Astrophysics and Space Science
 Pub Date:
 July 1991
 DOI:
 10.1007/BF00639094
 Bibcode:
 1991Ap&SS.181..267K
 Keywords:

 Bouguer Law;
 Laplace Transformation;
 Operators (Mathematics);
 Radiative Transfer;
 Singularity (Mathematics);
 Transfer Functions;
 Boundary Conditions;
 Integral Equations;
 Linear Equations;
 Roots Of Equations;
 Physics (General)