L2-Hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2020

L2-Hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system

Lanoir Addala
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  • PersonId : 1055070
M Lazhar Tayeb
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  • PersonId : 1055071

Résumé

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.
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Dates et versions

hal-02299535 , version 1 (27-09-2019)
hal-02299535 , version 2 (07-10-2019)
hal-02299535 , version 3 (31-12-2020)
hal-02299535 , version 4 (10-05-2021)

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Citer

Lanoir Addala, Jean Dolbeault, Xingyu Li, M Lazhar Tayeb. L2-Hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system. 2020. ⟨hal-02299535v3⟩
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