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Fundamental solutions for the anisotropic neutron transport equation†

Published online by Cambridge University Press:  14 November 2011

Joseph G. Conlon
Joseph G. Conlon
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri, U.S.A.
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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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 81 , Issue 3-4 , 1978 , pp. 325 - 350
Copyright
Copyright © Royal Society of Edinburgh 1978

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