L. Chen, E. Daus, A. Holzinger, A. Jüngel:

"Rigorous derivation of population cross-diffusion systems from moderately interacting particle systems";

in: "ASC Report 27/2020", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2020, ISBN: 978-3-902627-13-1, 1 - 33.

Population cross-diﬀusion systems of Shigesada-Kawasaki-Teramoto type

are derived in a mean-ﬁeld-type limit from stochastic, moderately interacting many-particle systems for multiple population species in the whole space. The diﬀusion term in the stochastic model depends nonlinearly on the interactions between the individuals,

and the drift term is the gradient of the environmental potential. In the ﬁrst step, the mean-ﬁeld limit leads to an intermediate nonlocal model. The local cross-diﬀusion system is derived in the second step in a moderate scaling regime, when the interaction potentials approach the Dirac delta distribution. The global existence of strong solutions to the intermediate and the local diﬀusion systems is proved for suﬃciently small initial data. Furthermore, numerical simulations on the particle level are presented.

Moderately interacting particle systems, stochastic particle systems, cross-diﬀusion system, rigorous derivation, Shigesada-Kawasaki-Teramoto model, mean-ﬁeld limit, population dynamics.

http://www.asc.tuwien.ac.at/preprint/2020/asc27x2020.pdf

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