I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2002, VOLUME 8, NUMBER 1, PAGES 97-115
A. V. Latyshev
A. V. Moiseev
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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
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.
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Last modified: July 5, 2002