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Spectral analysis of transport equations with bounce-back boundary conditions

✍ Scribed by K. Latrach; B. Lods

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
169 KB
Volume
32
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We investigate the spectral properties of the time‐dependent linear transport equation with bounce‐back boundary conditions. A fine analysis of the spectrum of the streaming operator is given and the explicit expression of the strongly continuous streaming semigroup is derived. Next, making use of a recent result from Sbihi (J. Evol. Equations 2007; 7:689–711), we prove, via a compactness argument, that the essential spectrum of the transport semigroup and that of the streaming semigroup coincide on all L^p^‐spaces with 1<p<∞. Application to the linear Boltzmann equation for granular gases is provided. Copyright © 2008 John Wiley & Sons, Ltd.

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