Convergence in the mean of solutions to the neutron integral Boltzmann equation in three‐dimensional systems

The Neumann series solution as well as practical solutions for the stationary integral Boltzmann equation, which governs the flux distribution of monoenergetic neutrons in a three‐dimensional system made by an isotropically scattering and multiplying material, are built up by extensively using the c...

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Bibliographic Details
Published in:Journal of mathematical physics 1973-03, Vol.14 (3), p.346-352
Main Authors: Boffi, V. C., Premuda, F., Spiga, G.
Format: Article
Language:English
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Summary:The Neumann series solution as well as practical solutions for the stationary integral Boltzmann equation, which governs the flux distribution of monoenergetic neutrons in a three‐dimensional system made by an isotropically scattering and multiplying material, are built up by extensively using the concept of double norm and the theory of bounded linear integral transformations in a Lebesgue space Lp . The convergence in the mean as well as other basic properties of the proposed solutions are studied for the cases of both distributed and isotropic deltalike sources.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1666320