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2018 The Vlasov-Fokker-Planck equation in non-convex landscapes: convergence to equilibrium
Manh Hong Duong, Julian Tugaut
Electron. Commun. Probab. 23: 1-10 (2018). DOI: 10.1214/18-ECP116

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.

Citation

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Manh Hong Duong. Julian Tugaut. "The Vlasov-Fokker-Planck equation in non-convex landscapes: convergence to equilibrium." Electron. Commun. Probab. 23 1 - 10, 2018. https://doi.org/10.1214/18-ECP116

Information

Received: 23 August 2017; Accepted: 5 February 2018; Published: 2018
First available in Project Euclid: 15 March 2018

zbMATH: 1387.60089
MathSciNet: MR3779816
Digital Object Identifier: 10.1214/18-ECP116

Subjects:
Primary: 35B40, 60H10
Secondary: 35K55, 60G10, 60J60

JOURNAL ARTICLE
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