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.

Deterministic particle approximation of scalar conservation laws

Rosini, M. D.
2017

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.
2017
Di Francesco, M.; Fagioli, S.; Rosini, M. D.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2380944
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