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Springer Verlag, Journal of Statistical Physics, 1(184), 2021

DOI: 10.1007/s10955-021-02784-4

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$\text {L}^2$-Hypocoercivity and Large Time Asymptotics of the Linearized Vlasov–Poisson–Fokker–Planck System

Journal article published in 2021 by Lanoir Addala, Jean Dolbeault ORCID, Xingyu Li, M. Lazhar Tayeb
This paper is available in a repository.
This paper is available in a repository.

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Abstract

This paper is devoted to the linearized Vlasov–Poisson–Fokker–Planck system in presence of an external potential of confinement. We investigate the large time behaviour of the solutions using hypocoercivity methods and a notion of scalar product adapted to the presence of a Poisson coupling. Our framework provides estimates which are uniform in the diffusion limit. As an application in a simple case, we study the one-dimensional case and prove the exponential convergence of the nonlinear Vlasov–Poisson–Fokker–Planck system without any small mass assumption.