Spectral theory and differential operators
Spectral theory and differential operators
One-parameter semigroups of postive operators
One-parameter semigroups of postive operators
Study of the Streaming Operator with General Maxwell's Boundary Conditions
Journal of Dynamical and Control Systems
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In this paper, we complete “Generation theorem for the streaming operator in slab geometry,” where we have proved that the one-dimensional streaming operator in slab domain, with general boundary conditions described by a linear operator K, generates a strongly continuous semigroup. Here, under the positivity and irreducibility of the boundary operator K, we prove the positivity and the irreducibility of the generated semigroup. We also study the spectral properties of the streaming operator and characterize its spectral bound. Under the compactness of the boundary operator K, we determine the essential type of the generated semigroup and find its behavior asymptotic in the operator norm topology.