The Vlasov-Fokker-Planck equation in non-convex landscapes: convergence to equilibrium
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Published version
Author(s)
Duong, MH
Tugaut, J
Type
Journal Article
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.
Date Issued
2018-03-15
Date Acceptance
2018-02-05
ISSN
1083-589X
Publisher
Institute of Mathematical Statistics
Journal / Book Title
Electronic Communications in Probability
Volume
23
Copyright Statement
© 2018 The Authors. Available under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).
Identifier
https://doi.org/10.1214/18-ECP116
Subjects
Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
kinetic equation
Vlasov-Fokker-Planck equation
free-energy
asymptotic behaviour
granular media equation
stochastic processes
SELF-STABILIZING PROCESSES
MULTI-WELLS LANDSCAPE
GRANULAR MEDIA
BEHAVIOR
FIELD
MODEL
0104 Statistics
Notes
pno: 19
Publication Status
Published
Article Number
19
Date Publish Online
2018-03-15