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

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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