Spectral properties of general advection operators and weighted translation semigroups

Abstract

International audienceWe 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

Spectral theory and time asymptotics of size-structured two-phase population models

“…MUSTAPHA MOKHTAR-KHARROUBI AND QUENTIN RICHARD Remark 7. We suspect that the spectra of A 1 µ , A 2 c2 and B are invariant by translation along the imaginary axis (and therefore are half-spaces), in the spirit of [18]. We conjecture also that their spectrum consist of essential spectrum only.…”