Contributions to Books:

E. Daus, M. Ptashnyk, C. Raithel:
"Derivation of a fractional cross-diffusion system as the limit of a stochastic many-particle system driven by Lévy noise";
in: "ASC Report 43/2020", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2020, ISBN: 978-3-902627-13-1, 1 - 30.

English 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 L´evy 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 K. Oelschl¨ager, in 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 is proved for the regularized macroscopic system, which then yields the same results for the non-regularized fractional cross-diffusion system in the limit.

Stochastic many-particle systems, fractional diffusion, cross-diffusion systems, L´evy processes

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.