Derivation of a fractional cross-diffusion system as the limit of a stochastic many-particle system driven by Lévy noise

Esther S. Daus, Mariya Ptashnyk, Claudia Raithel

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1 Citation (Scopus)

Abstract

In this article a fractional cross-diffusion system is derived as the rigorous many-particle limit of a multi-species system of moderately interacting particles that is driven by Lévy noise. The form of the mutual interaction is motivated by the porous medium equation with fractional potential pressure. Our approach is based on the techniques developed by Oelschläger (1989) and Stevens (2000), in the latter of which the convergence of a regularization of the empirical measure to the solution of a correspondingly regularized macroscopic system is shown. A well-posedness result and the non-negativity of solutions are proved for the regularized macroscopic system, which then yields the same results for the non-regularized fractional cross-diffusion system in the limit.
Original languageEnglish
Pages (from-to)386-426
Number of pages41
JournalJournal of Differential Equations
Volume309
Early online date1 Dec 2021
DOIs
Publication statusPublished - 5 Feb 2022

Keywords

  • Cross-diffusion systems
  • Fractional diffusion
  • Lévy processes
  • Stochastic many-particle systems

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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