Abstract
To investigate asymptotic phenomena in radiation transport problems in elongated, convex, vertically homogeneous, cylindrical regions, an equation is constructed which is similar to the transport equation in one-dimensional cylindrical geometry. It plays the role of the characteristic equation. Using the theory of completely continuous operators, the spectrum of the equation is studied, and the properties of the first eigenvalue are establishing as a function of the asymptotic parameter k≡ (−1, +1). Analysis of these properties implies that the characteristic equation is solvable at least in problems with isotropic scattering, provided the cross-sectional diameter of the region is sufficiently large.
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