Calculus of Variations and Geometric Measure Theory

S. Daneri - E. Radici - E. Runa

Deterministic particle approximation of aggregation-diffusion equations on unbounded domains

created by daneri on 04 Dec 2020
modified by radici on 22 Jan 2021


Submitted Paper

Inserted: 4 dec 2020
Last Updated: 22 jan 2021

Year: 2020

ArXiv: 2012.01966 PDF


We consider an aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions.

We prove that the fully deterministic particle approximations introduced in~\cite{DiFrancesco-Rosini} starting from general bounded initial densities converge to bounded weak solutions of the PDE. $L^\infty$-bounds for the approximating densities are obtained even in the case of short-range attractive kernels neither imposing hard constraints on the density functions nor nonlinear mobility conditions. Moreover, the convergence of the scheme is achieved in the whole space.