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arXiv · 0806.1035

Spectral analysis of transport equations with bounce-back boundary conditions

Khalid Latrach·Bertrand Lods
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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 M. Sbihi \cite{Sbihi}, 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 $1<p<\infty$.

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Khalid Latrach, Bertrand Lods. 2008-06-05. Spectral analysis of transport equations with bounce-back boundary conditions. https://doi.org/10.1002/mma.1088

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