Existence, stability and regularity of periodic solutions for nonlinear Fokker-Planck equations

2021/07/06 by Éric Luçon, Luçon, Eric, Christophe Poquet +1
Mathematics · Physics and Astronomy · #35K55 #35Q84 #37N25 #60K35 #82C31 #92B20 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Mechanics and Entropy

paper · doi:10.48550/arxiv.2107.02468

openalex publication_date 2021/07/06 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We consider a class of nonlinear Fokker-Planck equations describing the dynamics of an infinite population of units within mean-field interaction. Relying on a slow-fast viewpoint and on the theory of approximately invariant manifolds we obtain the existence of a stable periodic solution for the PDE, consisting of probability measures. Moreover we establish the existence of a smooth isochron map in the neighborhood of this periodic solution.

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