L. Chen, E. Daus, A. Jüngel:

"Rigorous mean-field limit and cross diffusion";

in: "ASC Report 30/2018", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2018, ISBN: 978-3-902627-11-7, 1 - 22.

The mean-ﬁeld limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diﬀusion equations, modeling the segregation of populations. The mean-ﬁeld limit is performed in two steps: First, the many-particle system leads in the large population limit to an intermediate nonlocal diﬀusion system. The local cross-diﬀusion system is then obtained from the nonlocal system when the interaction potentials approach the Dirac delta distribution. The global existence of the limiting and the intermediate diﬀusion systems is shown for small initial data, and an error estimate is given.

Interacting particle system, stochastic processes, cross-diﬀusion system, mean-ﬁeld equations, mean-ﬁeld limit, population

http://www.asc.tuwien.ac.at/preprint/2018/asc30x2018.pdf

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