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A spectral representation of the linear multivelocity transport problem

A spectral representation of the linear multivelocity transport problem Abstract The transformation of the original characteristic equation of the multivelocity linear transport theory was carried out by expanding the scattering function for the problem to be solved as a spectral integral over a complete set of eigenfunctions for the previously solved transport problem. The obtained equation represents a singular integral equation containing a spectral integral over the spectrum of the solved problem, whose kernel depends on the difference between the scattering of the problem to be solved and that of the already solved problem. We consider also the examples illustrating the validity of such a transformation. M. Kanal and J. Davies made a similar transformation of the characteristic equation of the one-velocity transport theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

A spectral representation of the linear multivelocity transport problem

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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
1072-947X
eISSN
1572-9176
DOI
10.1515/gmj-2016-0033
Publisher site
See Article on Publisher Site

Abstract

Abstract The transformation of the original characteristic equation of the multivelocity linear transport theory was carried out by expanding the scattering function for the problem to be solved as a spectral integral over a complete set of eigenfunctions for the previously solved transport problem. The obtained equation represents a singular integral equation containing a spectral integral over the spectrum of the solved problem, whose kernel depends on the difference between the scattering of the problem to be solved and that of the already solved problem. We consider also the examples illustrating the validity of such a transformation. M. Kanal and J. Davies made a similar transformation of the characteristic equation of the one-velocity transport theory.

Journal

Georgian Mathematical Journalde Gruyter

Published: Sep 1, 2016

References