Spectral analysis of transport equations with bounce-back boundary conditions

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 $1<p<\infty$.

References in corpus (3)

• The dissipative linear Boltzmann equation for hard spheres
• Integral representation of the linear Boltzmann operator for granular gas dynamics with applications
• Stability of the essential spectrum for 2D--transport models with Maxwell boundary conditions

Cited by in corpus (1)

• Transport equations and perturbations of boundary conditions