Deterministic particle approximation of scalar conservation laws
Analysis of PDEs
2016-05-20 v1
Abstract
In this paper we prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the large particle limit of a microscopic follow-the-leader type model, which is interpreted as the discrete Lagrangian approximation of the nonlinear scalar conservation law. The result is complemented with some numerical simulations.
Cite
@article{arxiv.1605.05883,
title = {Deterministic particle approximation of scalar conservation laws},
author = {Marco Di Francesco and Simone Fagioli and Massimiliano D. Rosini},
journal= {arXiv preprint arXiv:1605.05883},
year = {2016}
}