Abstract
SynopsisWe 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.
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Schedule a callMore From: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
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