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arXiv · 1505.01212

Stationary solutions of the Vlasov-Fokker-Planck equation: existence, characterization and phase-transition

Manh Hong Duong·Julian Tugaut
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Abstract

In this paper, we study the set of stationary solutions of the Vlasov-Fokker-Planck (VFP) equation. This equation describes the time evolution of the probability distribution of a particle moving under the influence of a double-well potential, an interaction potential, a friction force and a stochastic force. We prove, under suitable assumptions, that the VFP equation does not have a unique stationary solution and that there exists a phase transition. Our study relies on the recent results by Tugaut and coauthors regarding the McKean-Vlasov equation.

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Manh Hong Duong, Julian Tugaut. 2015-05-05. Stationary solutions of the Vlasov-Fokker-Planck equation: existence, characterization and phase-transition. https://arxiv.org/abs/1505.01212

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