n this paper, we consider the long time behaviour of collisionless kinetic equation with stochastic diffuse boundary operators for velocities bounded away from zero. We show that under suitable reasonable conditions, the semigroup is eventually compact. In particular, without any irreducibility assumption, the semigroup converges exponentially to the spectral projection associated to the zero eigenvalue as t→∞. This contrasts drastically to the case allowing arbitrarily slow velocities for which the absence of a spectral gap yields at most algebraic rate of convergence to equilibrium. Some open questions are also mentioned

On eventual compactness of collisionless kinetic semigroups with velocities bounded away from zero

Bertrand Lods
First
;
2022-01-01

Abstract

n this paper, we consider the long time behaviour of collisionless kinetic equation with stochastic diffuse boundary operators for velocities bounded away from zero. We show that under suitable reasonable conditions, the semigroup is eventually compact. In particular, without any irreducibility assumption, the semigroup converges exponentially to the spectral projection associated to the zero eigenvalue as t→∞. This contrasts drastically to the case allowing arbitrarily slow velocities for which the absence of a spectral gap yields at most algebraic rate of convergence to equilibrium. Some open questions are also mentioned
2022
22
1
1
36
https://arxiv.org/abs/2105.09662
Bertrand Lods; Mustapha Mokhtar-Kharroubi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1850227
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