Fine Spectral Analysis of Isotropic Partly Elastic Neutron Transport Operators |
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Authors: | Mustapha Mokhtar-Kharroubi Yahya Mohamed |
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Affiliation: | 1.Laboratoire de Mathématiques, CNRS-UMR 6623,Université de Bourgogne Franche-Comté,Besan?on,France;2.Institut National Universitaire Jean-Fran?ois Champollion,Albi Cedex,France |
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Abstract: | This paper deals with spectral theory of a new class of neutron transport operators involving collision operators of the form (K=K_{i}+K_{e}) where (K_{i}) (resp. (K_{e})) describes the inelastic (resp. elastic) collisions of neutrons with the host material. We give a fine analysis of their asymptotic point spectra for isotropic space homogeneous cross sections in bounded geometries. We provide a new formalism relying on spectral analysis of some non compact symmetrizable operators arising in transport theory. Additional results on essential spectra are also given. |
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