Spectral properties of general advection operators and weighted translation semigroups

Bertrand Lods (1) , Mustapha Mokhtar-Kharroubi (2) , Mohammed Sbihi (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

We investigate the spectral properties of a class of weighted shift semigroups associated to abstract transport equations with a Lipschitz--continuous vector field with no--reentry boundary conditions. We illustrate our results with various examples taken from collisionless kinetic theory.

Mots clés: Spectral Mapping Theorem; weighted shift; Annular Hull Theorem; transport equation

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

Bertrand Lods, Mustapha Mokhtar-Kharroubi, Mohammed Sbihi. Spectral properties of general advection operators and weighted translation semigroups. Communications on Pure and Applied Mathematics, 2009, 8 (5), pp.1469-1492. ⟨10.3934/cpaa.2009.8.1469⟩. ⟨hal-00281711v2⟩