L2-Hypocoercivity and Large Time Asymptotics of the Linearized Vlasov-Poisson-Fokker-Planck System

被引：0
作者：
Addala, Lanoir [1 ]
Dolbeault, Jean [2 ]
Li, Xingyu [2 ]
Tayeb, M. Lazhar [3 ]
机构：
[1] Univ Carthage, Fac Sci Bizerte, Dept Math, Zarzouna 7021, Banzart, Tunisia
[2] Univ Paris 09, PSL Res Univ, CEREMADE, CNRS,UMR N 7534, Pl Lattre Tassigny, F-75775 Paris 16, France
[3] Univ Tunis El Manar, Fac Sci Tunis, Dept Math, El Manar 2092, Tunisia
来源：
JOURNAL OF STATISTICAL PHYSICS | 2021年 / 184卷 / 01期
关键词：
Confinement; Vlasov-Poisson-Fokker-Planck system; Convergence; Large-time behavior; Rate of convergence; Hypocoercivity; Diffusion limit; FAST DIFFUSION EQUATION; KINETIC-EQUATIONS; SOBOLEV INEQUALITIES; BEHAVIOR; LIMIT; EQUILIBRIUM; HYPOCOERCIVITY; CONVERGENCE; CONSTANTS; STATES;
D O I：
10.1007/s10955-021-02784-4
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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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页数：34
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