The finite Laplace transform for solving a weakly singular integral equation occurring in transfer theory
Astrophysics
2007-05-23 v1
Abstract
We solve a weakly singular integral equation by Laplace transformation over a finite interval of R. The equation is transformed into a Cauchy integral equation, whose resolution amounts to solving two Fredholm integral equations of the second kind with regular kernels. This classical scheme is used to clarify the emergence of the auxiliary functions expressing the solution of the problem. There are four such functions, two of them being classical ones. This problem is encountered while studying the propagation of light in strongly scattering media such as stellar atmospheres.
Keywords
Cite
@article{arxiv.astro-ph/0601343,
title = {The finite Laplace transform for solving a weakly singular integral equation occurring in transfer theory},
author = {B. Rutily and L. Chevallier},
journal= {arXiv preprint arXiv:astro-ph/0601343},
year = {2007}
}
Comments
17 pages, 5 figures, Journal of Integral Equations and Applications, accepted 19 December 2004