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arXiv · 2107.02468

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

Eric Luçon·Christophe Poquet
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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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Eric Luçon, Christophe Poquet. 2021-07-06. Existence, stability and regularity of periodic solutions for nonlinear Fokker-Planck equations. https://arxiv.org/abs/2107.02468

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