SPECTRAL ANALYSIS OF TRANSPORT EQUATIONS WITH BOUNCE-BACK BOUNDARY CONDITIONS.
Khalid Latrach, Bertrand Lods, Université Blaise Pascal (clermont Ii · 2013
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 [1], 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 <∞.