Long time behaviour and particle approximation of a generalised Vlasov dynamic

Manh Hong Duong

doi:10.1016/j.na.2015.06.018

Long time behaviour and particle approximation of a generalised Vlasov dynamic

Manh Hong Duong

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In this paper, we are interested in a generalised Vlasov equation, which describes the evolution of the probability density of a particle evolving according to a generalised Vlasov dynamic. The achievement of the paper is twofold. Firstly, we obtain a quantitative rate of convergence to the stationary solution in the Wasserstein metric. Secondly, we provide a many-particle approximation for the equation and show that the approximate system satisfies the propagation of chaos property.

Original language	English
Pages (from-to)	1-16
Number of pages	16
Journal	Nonlinear Analysis: Theory, Methods & Applications
Volume	127
Early online date	7 Jul 2015
DOIs	https://doi.org/10.1016/j.na.2015.06.018
Publication status	Published - Nov 2015

Keywords

Long time behaviour
Particle approximation
propagation of chaos
Generalised Vlasov dynamic
Wasserstein metric

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Cite this

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title = "Long time behaviour and particle approximation of a generalised Vlasov dynamic",

abstract = "In this paper, we are interested in a generalised Vlasov equation, which describes the evolution of the probability density of a particle evolving according to a generalised Vlasov dynamic. The achievement of the paper is twofold. Firstly, we obtain a quantitative rate of convergence to the stationary solution in the Wasserstein metric. Secondly, we provide a many-particle approximation for the equation and show that the approximate system satisfies the propagation of chaos property.",

keywords = "Long time behaviour, Particle approximation, propagation of chaos, Generalised Vlasov dynamic, Wasserstein metric",

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AB - In this paper, we are interested in a generalised Vlasov equation, which describes the evolution of the probability density of a particle evolving according to a generalised Vlasov dynamic. The achievement of the paper is twofold. Firstly, we obtain a quantitative rate of convergence to the stationary solution in the Wasserstein metric. Secondly, we provide a many-particle approximation for the equation and show that the approximate system satisfies the propagation of chaos property.

KW - Long time behaviour

KW - Particle approximation

KW - propagation of chaos

KW - Generalised Vlasov dynamic

KW - Wasserstein metric

U2 - 10.1016/j.na.2015.06.018

DO - 10.1016/j.na.2015.06.018

M3 - Article

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VL - 127

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EP - 16

JO - Nonlinear Analysis: Theory, Methods & Applications

JF - Nonlinear Analysis: Theory, Methods & Applications

ER -

Long time behaviour and particle approximation of a generalised Vlasov dynamic

Abstract

Keywords

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