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On singular mono-energetic transport equations in slab geometry

✍ Scribed by Mohamed Chabi; Khalid Latrach

Book ID
102510971
Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
202 KB
Volume
25
Category
Article
ISSN
0170-4214

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✦ Synopsis

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 Β© 2002 John Wiley & Sons, Ltd.

πŸ“œ SIMILAR VOLUMES

Spectral properties and regularity of so
Spectral properties and regularity of solutions to transport equations in slab geometry
✍ Khalid Latrach; Hatem Megdiche πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 285 KB

## Abstract This paper deals with regularity properties of solutions to Cauchy problems governed by one‐dimensional transport equations for a wide class of anisotropic scattering operators and a variety of boundary conditions which cover, in particular, the classical known ones. Under adequate assu