Orateur
Description
In the field of population dynamics, cross-diffusion partial differential equations have gained more impact, see for instance the SKT-model by Shigesada–Kawasaki–Teramoto. However, a rigorous derivation starting from a stochastic many-particle system was still missing in the literature.
In this talk, I will show how the approach of moderately interacting particles in the meanfield limit can be used in order to derive cross-diffusion models of SKT-type starting from a stochastic interacting many-particle system.
As a byproduct of the mean-field derivation, we also study a non-local version of the underlying PDE models. These non-local PDEs represent an intermediate level between the particle
dynamics and the final cross-diffusion partial differential equation.
This talk is based on the joint work with Li Chen, Esther Daus and Ansgar Jungel "Rigorous derivation of population cross-diffusion systems from moderately interacting particle systems", Journal of Nonlinear Science, 31(6), 1-38 (2021).
