We are concerned in this talk with the exponential stabilisation (spectral
gap) for linear kinetic equations with degenerate thermalisation, i.e. when the
collision operator vanishes on parts of the spatial domain. The method
covers both scattering and Fokker-Planck type operators, and deals with external
potential and boundary conditions, but in these talk we present only its core
argument and restrict ourselves to the kinetic Fokker-Planck in the periodic torus
with unit velocities and a thermalisation degeneracy. This is a joint work with
Helge Dietert, Harsha Hutridurga and Clément Mouhot.
Romain Duboscq, Ariane Trescases
