Convergence of the follow-the-leader scheme for scalar conservation laws with space dependent flux

Marco Di Francesco; Graziano Stivaletta

doi:10.3934/dcds.2020010

Article Contents

2020, Volume 40, Issue 1: 233-266. Doi: 10.3934/dcds.2020010

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$ L^{2} $

initial data

Convergence of the follow-the-leader scheme for scalar conservation laws with space dependent flux

Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, Via Vetoio 1, Coppito, I-67100 L'Aquila, Italy

Received: January 2019

Revised: May 2019

Published: October 2019

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Abstract

This paper deals with the derivation of entropy solutions to Cauchy problems for a class of scalar conservation laws with space-density depending fluxes from systems of deterministic particles of follow-the-leader type. We consider fluxes which are product of a function of the density $ v(\rho) $ and a function of the space variable $ \phi(x) $. We cover four distinct cases in terms of the sign of $ \phi $, including cases in which the latter is not constant. The convergence result relies on a local maximum principle and on a uniform $ BV $ estimate for the approximating density.

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Mathematics Subject Classification: Primary: 35L65, 35F25; Secondary: 82C22, 90B20.

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