FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 1, PAGES 97-115

The boundary-value problem for the equations of radiation transfer of polarized light

A. V. Latyshev
A. V. Moiseev

Abstract

View as HTML     View as gif image    View as LaTeX source

The theory of the solution of half-space boundary-value problems for Chandrasekhar's equations describing the scattering of polarized light in the case of a combination of Rayleigh and isotropic scattering with arbitrary photon survival probability in an elementary scattering is constructed. A theorem on the expansion of the solution in terms of eigenvectors of discrete and continuous spectra is proved. The proof reduces to solving the Riemann--Hilbert vector boundary-value problem with a matrix coefficient. The matrix that reduces the coefficient to diagonal form has eight branch points in the complex plain. The definition of an analytical branch of a diagonalizing matrix gives us the opportunity to reduce the Riemann--Hilbert vector boundary-value problem to two scalar boundary-value problems on the major cut $[0,1]$ and two vector boundary-value problems on the supplementary cut.

The solution of the Riemann--Hilbert boundary-value problem is given in the class of meromorphic vectors. The solvability conditions enable unique determination of the unknown coefficients of the expansion and the free parameters of the solution.

All articles are published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k02/k021/k02109h.htm
Last modified: July 5, 2002