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Fundamental solutions for the anisotropic neutron transport equation

Published online by Cambridge University Press:  14 November 2011

Joseph G. Conlon
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri, U.S.A.

Synopsis

We construct a fundamental solution for the n dimensional time independent anisotropic neutron transport equation. This is an operator valued distribution G(x) with a singularity at the origin. By estimating G(x) we are able to construct smooth solutions to the transport equation. We are also able to derive in a straightforward fashion results of Birkhoff and Abu-Shumays on the existence of harmonic solutions to the isotropic transport equation. When n = 1, G(x) is a function which is continuous except at x = 0. We show that the classical formula for the jump of G(x) at the origin is equivalent to the completeness of Case's full range eigenfunction expansion.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1978

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