Calculus of Variations and Geometric Measure Theory

E. Radici - F. Stra

Entropy solutions of non-local scalar conservation laws with congestion via deterministic particle method

created by stra on 03 Sep 2021
modified by radici on 05 Jun 2024


Published Paper

Inserted: 3 sep 2021
Last Updated: 5 jun 2024

Journal: SIAM: Journal of Math. Anal.
Year: 2023

ArXiv: 2107.10760 PDF


We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general assumptions that the existing literature: the velocity fields are less regular (in particular the interaction force can have a discontinuity at the origin) with no prescribed attractive/repulsive regime and the mobility can have unbounded support. We complement our results with some numerical simulations, among which we show the applicability of the schemes to the multi-species setting.