Spectral analysis of transport equations with bounce‐back boundary conditions
K. Latrach, B. Lods
Source abstract
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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