English

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

Analysis of PDEs 2021-07-07 v1 Probability

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.

Keywords

Cite

@article{arxiv.2107.02468,
  title  = {Existence, stability and regularity of periodic solutions for nonlinear Fokker-Planck equations},
  author = {Eric Luçon and Christophe Poquet},
  journal= {arXiv preprint arXiv:2107.02468},
  year   = {2021}
}

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37 pages