The notion of propagation of chaos for large systems of interacting particles originates in
statistical physics and has recently become a central notion in many areas of applied …

We show that degenerate nonlinear diffusion equations can be asymptotically obtained as a
limit from a class of nonlocal partial differential equations. The nonlocal equations are …

This paper studies the derivation of the quadratic porous medium equation and a class of
cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a …

The Dean-Kawasaki equation-one of the most fundamental SPDEs of fluctuating
hydrodynamics-has been proposed as a model for density fluctuations in weakly interacting …

A mean-field-type limit from stochastic moderately interacting many-particle systems with
singular Riesz potential is performed, leading to nonlocal porous-medium equations in the …

The aim of this paper is to provide the analysis result for the partial differential equations
arising from the rigorous derivation of the degenerate parabolic-elliptic Keller-Segel system …

Some results on cross-diffusion systems with entropy structure are reviewed. The focus is on
local-in-time existence results for general systems with normally elliptic diffusion operators …

We construct deterministic particle solutions for linear and fast diffusion equations using a
nonlocal approximation. We exploit the $2 $-Wasserstein gradient flow structure of the …

A central limit theorem is shown for moderately interacting particles in the whole space. The
interaction potential approximates singular attractive or repulsive potentials of sub-Coulomb …

In this paper we analyse a finite volume scheme for a nonlocal version of the Shigesada–
Kawazaki–Teramoto (SKT) cross-diffusion system. We prove the existence of solutions to the …