Calculus of Variations and Geometric Measure Theory
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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

[BibTeX]

preprint

Inserted: 3 sep 2021
Last Updated: 3 sep 2021

Year: 2021

ArXiv: 2107.10760 PDF

Abstract:

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.

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