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Study of the Free Streaming Operator in Slab Geometry in Dependence of the Boundary Conditions

✍ Scribed by Silvia Totaro

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 301 KB
Volume: 20
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(19970525)20:8<717::aid-mma884>3.0.co;2-8

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✦ Synopsis

Communicated by G. F. Roach

We study the free streaming operator ¹ in a slab domain with boundary conditions described by a linear matrix operator acting between the 'incoming' and 'outgoing' particle fluxes. Under suitable assumptions on the entries of , it is proved that the resolvent operator of ¹ is positive. It is proved also that ¹ is the generator of a positive strongly continuous semigroup, whose type depends on the norm of the entries of . Some examples are given. In particular the case of Maxwell type boundary conditions is studied and the location of the spectrum of ¹ is improved.

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