Published Paper

Inserted: 4 dec 2020
Last Updated: 28 oct 2022

Journal: Journal of Differential Equations
Year: 2022

Abstract:

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.