Geodesic
Some spectral properties of the streaming operator with general boundary conditions
Applications of Mathematics, Tome 53 (2008) no. 1, pp. 1-12.

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This paper deals with the spectral study of the streaming operator with general boundary conditions defined by means of a boundary operator $K$. We study the positivity and the irreducibility of the generated semigroup proved in [M. Boulanouar, L’opérateur d’Advection: existence d’un $C_0$-semi-groupe (I), Transp. Theory Stat. Phys. 31, 2002, 153–167], in the case $\Vert K\Vert \ge 1$. We also give some spectral properties of the streaming operator and we characterize the type of the generated semigroup in terms of the solution of a characteristic equation.
DOI : 10.1007/s10492-008-0010-4
Classification : 47D06, 47G20, 47N50, 82C70
Keywords: compactness; essential type; positivity and irreducibility; spectral properties; streaming operator; strongly continuous semigroups 
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Boulanouar, Mohamed. Some spectral properties of the streaming operator with general boundary conditions. Applications of Mathematics, Tome 53 (2008) no. 1, pp. 1-12. doi : 10.1007/s10492-008-0010-4. http://geodesic.mathdoc.fr/articles/10.1007/s10492-008-0010-4/

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