On singular mono‐energetic transport equations in slab geometry
Mohamed Chabi, Khalid Latrach
Source abstract
Abstract In this paper we establish the well posedness of the Cauchy problem associated to transport equations with singular cross‐sections (i.e. unbounded collisions frequencies and unbounded collision operators) in L 1 spaces for specular reflecting boundary conditions. In addition, we discuss the weak compactness of the second‐order remainder term of the Dyson–Phillips expansion. This allows us to estimate the essential type of the transport semigroup from which the asymptotic behaviour of the solution is derived. The case of singular transport equations with periodic boundary conditions is also discussed. The proofs make use of the Miyadera perturbation theory of positive semigroups on AL ‐spaces. Copyright © 2002 John Wiley & Sons, Ltd.
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