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.
Keywords: Vlasov–Fokker–Planck equations, Interacting particles, Inelastic Lorentz gas, Relaxation to equilibrium, Hypocoercivity
@article{AIHPC_2017__34_7_1727_0, author = {Alonso, Ricardo and Goudon, Thierry and Vavasseur, Arthur}, title = {Damping of particles interacting with a vibrating medium}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1727--1758}, publisher = {Elsevier}, volume = {34}, number = {7}, year = {2017}, doi = {10.1016/j.anihpc.2016.12.005}, mrnumber = {3724755}, zbl = {1386.82062}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2016.12.005/} }
TY - JOUR AU - Alonso, Ricardo AU - Goudon, Thierry AU - Vavasseur, Arthur TI - Damping of particles interacting with a vibrating medium JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 1727 EP - 1758 VL - 34 IS - 7 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2016.12.005/ DO - 10.1016/j.anihpc.2016.12.005 LA - en ID - AIHPC_2017__34_7_1727_0 ER -
%0 Journal Article %A Alonso, Ricardo %A Goudon, Thierry %A Vavasseur, Arthur %T Damping of particles interacting with a vibrating medium %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 1727-1758 %V 34 %N 7 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2016.12.005/ %R 10.1016/j.anihpc.2016.12.005 %G en %F AIHPC_2017__34_7_1727_0
Alonso, Ricardo; Goudon, Thierry; Vavasseur, Arthur. Damping of particles interacting with a vibrating medium. Annales de l'I.H.P. Analyse non linéaire, Volume 34 (2017) no. 7, pp. 1727-1758. doi : 10.1016/j.anihpc.2016.12.005. http://archive.numdam.org/articles/10.1016/j.anihpc.2016.12.005/
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