Spectral analysis of transport equations with bounce-back boundary conditions

Khalid Null Latrach (1) , Bertrand Lods (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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

Mots clés: compactness; Transport operator; bounce-back boudary conditions; transport semigroup; essential spectrum; compactness.

Domaines: Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Khalid Null Latrach, Bertrand Lods. Spectral analysis of transport equations with bounce-back boundary conditions. Mathematical Methods in the Applied Sciences, 2009, 32 (11), pp.1325 - 1344. ⟨10.1002/mma.1088⟩. ⟨hal-00285598⟩