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Mean-field-type limits of interacting particle systems for multiple species

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Mean-field-type limits of interacting particle systems for multiple species
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19
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CC Attribution - NonCommercial - NoDerivatives 2.0 Generic:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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The aim of this talk is the rigorous derivation of cross-diffusion systems from stochastic, moderately interacting many-particle sys-tems for multiple species. Applications include animal populations and neuronal ensembles. The mean-field limit leads to nonlocal cross-diffusion systems, while the limit of vanishing interaction radius gives local cross-diffusionequations. This allows for the derivation of fluid-type models that can befound in neuronal networks and of Shigesada-Kawasaki-Teramoto populationmodels. The derivation uses the techniques of Oehlschl ̈ager. The entropystructure of the limiting models is discussed and some numerical experimentsare presented.
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