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Polarized light transfer above a reflecting surface
Author(s) -
van der Mee C. V. M.,
Neunzert H.
Publication year - 1986
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670080121
Subject(s) - mathematics , uniqueness , mathematical analysis , corollary , boundary value problem , integral equation , monotonic function , surface (topology) , reflection (computer programming) , uniqueness theorem for poisson's equation , completeness (order theory) , geometry , pure mathematics , programming language , computer science
The existence and uniqueness are established for the solution of the equation of transfer of polarized light in a homogeneous atmosphere of finite optical thickness, assuming reflection by the planetary surface. A general L p ‐space formulation is adopted. The boundary value problem is first written as a vector‐valued integral equation. Using monotonicity properties of the spectral radii of the integral operators involved as well as recent half‐range completeness results for kinetic equations with reflective boundary conditions, the present results follow as a corollary.