Convergence to equilibrium for a degenerate McKean-Vlasov Equation

Duong, Manh Hong; Einav, Amit

Abstract

In this work we study the convergence to equilibrium for a (po-tentially) 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.

Citation

Duong, M. H., & Einav, A. (2024). Convergence to equilibrium for a degenerate McKean-Vlasov Equation. Journal of Mathematical Physics, 65(12), https://doi.org/10.1063/5.0170283

• Journal Article Type: Article
• Acceptance Date: Nov 17, 2024
• Online Publication Date: Dec 17, 2024
• Publication Date: Dec 1, 2024
• Deposit Date: Nov 27, 2024
• Publicly Available Date: Dec 18, 2024
• Journal: Journal of Mathematical Physics
• Print ISSN: 0022-2488
• Electronic ISSN: 1089-7658
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 65
• Issue: 12
• DOI: https://doi.org/10.1063/5.0170283
• Keywords: McKean-Vlasov equation; Fokker-Planck equation; entropy; long
• Public URL: https://durham-repository.worktribe.com/output/3107407