Convergence to equilibrium for a degenerate Mckean-Vlasov equation

Manh Hong Duong; Amit Einav

doi:10.1063/5.0170283

Convergence to equilibrium for a degenerate Mckean-Vlasov equation

Manh Hong Duong
, Amit Einav^*

^*Corresponding author for this work

Mathematics

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Abstract

In this work we study the convergence to equilibrium for a (potentially) degenerate nonlinear and nonlocal McKean–Vlasov equation. We show that the solution to this equation is related to the solution of a linear degenerate and/or defective Fokker–Planck equation and employ recent sharp convergence results to obtain an easily computable (and many times sharp) rates of convergence to equilibrium for the equation in question.

Original language	English
Article number	121505
Number of pages	12
Journal	Journal of Mathematical Physics
Volume	65
Issue number	12
DOIs	https://doi.org/10.1063/5.0170283
Publication status	Published - 17 Dec 2024

Keywords

McKean-Vlasov equation
Fokker-Planck equation
entropy
long time behaviour

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10.1063/5.0170283Licence: Creative Commons: Attribution (CC BY)

DuongM2024ConvergenceFinal published version, 4.57 MBLicence: Creative Commons: Attribution (CC BY)

Rigorous coarse-graining of defects at positive temperature
Duong, H. (Principal Investigator)
Engineering & Physical Science Research Council
1/06/22 → 31/05/23
Project: Research Councils
Variational structures, convergence to equilibrium and multiscale analysis for non-Markovian systems
Duong, H. (Principal Investigator)
Engineering & Physical Science Research Council
1/02/22 → 30/06/24
Project: Research Councils

Cite this

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title = "Convergence to equilibrium for a degenerate Mckean-Vlasov equation",

abstract = "In this work we study the convergence to equilibrium for a (potentially) degenerate nonlinear and nonlocal McKean–Vlasov equation. We show that the solution to this equation is related to the solution of a linear degenerate and/or defective Fokker–Planck equation and employ recent sharp convergence results to obtain an easily computable (and many times sharp) rates of convergence to equilibrium for the equation in question.",

keywords = "McKean-Vlasov equation, Fokker-Planck equation, entropy, long time behaviour",

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AU - Einav, Amit

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N2 - In this work we study the convergence to equilibrium for a (potentially) degenerate nonlinear and nonlocal McKean–Vlasov equation. We show that the solution to this equation is related to the solution of a linear degenerate and/or defective Fokker–Planck equation and employ recent sharp convergence results to obtain an easily computable (and many times sharp) rates of convergence to equilibrium for the equation in question.

AB - In this work we study the convergence to equilibrium for a (potentially) degenerate nonlinear and nonlocal McKean–Vlasov equation. We show that the solution to this equation is related to the solution of a linear degenerate and/or defective Fokker–Planck equation and employ recent sharp convergence results to obtain an easily computable (and many times sharp) rates of convergence to equilibrium for the equation in question.

KW - McKean-Vlasov equation

KW - Fokker-Planck equation

KW - entropy

KW - long time behaviour

U2 - 10.1063/5.0170283

DO - 10.1063/5.0170283

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VL - 65

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

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Convergence to equilibrium for a degenerate Mckean-Vlasov equation

Abstract

Keywords

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Projects

Rigorous coarse-graining of defects at positive temperature

Variational structures, convergence to equilibrium and multiscale analysis for non-Markovian systems

Cite this