Geodesic
Damping of particles interacting with a vibrating medium
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 7, pp. 1727-1758

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We investigate the large time behavior of the solutions of a Vlasov–Fokker–Planck equation where particles are subjected to a confining external potential and a self-consistent potential intended to describe the interaction of the particles with their environment. The environment is seen as a medium vibrating in a direction transverse to particles' motion. We identify equilibrium states of the model and justify the asymptotic trend to equilibrium. The analysis relies on hypocoercivity techniques.

DOI : 10.1016/j.anihpc.2016.12.005
Classification : 82C70, 70F45, 37K05, 74A25
Keywords: Vlasov–Fokker–Planck equations, Interacting particles, Inelastic Lorentz gas, Relaxation to equilibrium, Hypocoercivity 
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     title = {Damping of particles interacting with a vibrating medium},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1727--1758},
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Alonso, Ricardo; Goudon, Thierry; Vavasseur, Arthur. Damping of particles interacting with a vibrating medium. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 7, pp. 1727-1758. doi: 10.1016/j.anihpc.2016.12.005

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