Study of the Streaming Operator with General Maxwell's Boundary Conditions

Abstract

We study the streaming operator in slab domain with general Maxwell's boundary conditions described by linear boundary operators K+ and K−. We prove that the streaming operator generates a strongly continuous semigroup. We show that the positivity and irreducibility of the boundary operators imply the positivity and irreducibility of the generated semigroup. We establish the spectral properties of the streaming operator and characterize its spectral bound. Under the compactness of boundary operators, we explicitly give the essential type of the generated semigroup and describe its asymptotic behavior in the operator norm topology.