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Keywords:
compactness; essential type; positivity and irreducibility; spectral properties; streaming operator; strongly continuous semigroups
compactness; essential type; positivity and irreducibility; spectral properties; streaming operator; strongly continuous semigroups
Summary:
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.
References:
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