Abstract
In this paper, we study the long-time behaviour of solutions to the Vlasov-Fokker-Planck equation where the confining potential is non-convex. This is a nonlocal nonlinear partial differential equation describing the time evolution of the probability distribution of a particle moving under the influence of a non-convex potential, an interaction potential, a friction force and a stochastic force. Using the free-energy approach, we show that under suitable assumptions solutions of the Vlasov-Fokker-Planck equation converge to an invariant probability.
Original language | English |
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Article number | 19 |
Number of pages | 10 |
Journal | Electronic Communications in Probability |
Volume | 23 |
DOIs | |
Publication status | Published - 15 Mar 2018 |
Keywords
- Kinetic equation
- Vlasov-Fokker-Planck equation
- Free-energy
- Asymptotic behaviour
- Granular media equation
- Stochastic processes