Calculus of Variations and Geometric Measure Theory

S. Daneri - E. Radici - E. Runa

Deterministic particle approximation of aggregation diffusion equations with nonlinear mobility

created by radici on 28 Oct 2022
modified on 05 Jun 2024


Published Paper

Inserted: 28 oct 2022
Last Updated: 5 jun 2024

Journal: Journal of Hyperbolic Differential Equations
Year: 2023

ArXiv: 2209.10884 PDF


We consider a class of aggregation-diffusion equations on unbounded one dimensional domains with Lipschitz nonincreasing mobility function. We show strong $L^1$-convergence of a suitable deterministic particle approximation to weak solutions of a class aggregation-diffusion PDEs (coinciding with the classical ones in the no vacuum regions) for any bounded initial data of finite energy. In order to prove well-posedness and convergence of the scheme with no BV or no vacuum assumptions and overcome the issues posed in this setting by the presence of a mobility function, we improve and strengthen the techniques introduced in arXiv:2012.01966(2).