Well-posedness results for superlinear Fokker-Planck equations

Stefano Buccheri; Fernando Farroni; Gabriella Zecca

Well-posedness results for superlinear Fokker-Planck equations

Analysis of PDEs 2026-01-15 v1

Authors: Stefano Buccheri , Fernando Farroni , Gabriella Zecca

Abstract

In this manuscript we deal with a class of nonlinear Fokker-Planck equations with the following structure $\partial_t u - \div\big(M\nabla u+ E h(u)\big)=0,$ with $M$ a bounded elliptic matrix, $E$ a vector field in a suitable Lebesgue space, and $h(u)$ featuring a superlinear growth for $u$ large. We provide existence results of $C([0,T),L^1)$ distributional solutions to initial-boundary value problems related to the equation above together with some qualitative properties of solutions.

Keywords

semilinear elliptic equations positive solutions of elliptic equations fokker-planck equation

Cite

@article{arxiv.2601.09341,
  title  = {Well-posedness results for superlinear Fokker-Planck equations},
  author = {Stefano Buccheri and Fernando Farroni and Gabriella Zecca},
  journal= {arXiv preprint arXiv:2601.09341},
  year   = {2026}
}

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