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Fundamental solutions for the anisotropic neutron transport equation†
Published online by Cambridge University Press: 14 November 2011
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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