Conservation laws with discontinuous flux

Mauro Garavello; Roberto Natalini; Benedetto Piccoli; Andrea Terracina

doi:10.3934/nhm.2007.2.159

Article Contents

2007, Volume 2, Issue 1: 159-179. Doi: 10.3934/nhm.2007.2.159

This issue Previous Article Existence and stability of entropy solutions for a conservation law with discontinuous non-convex fluxes Next Article Multiscale stochastic homogenization of monotone operators

Conservation laws with discontinuous flux

1.
Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via R. Cozzi 53 - Edificio U5, 20125 - Milano
2.
Istituto per le Applicazioni del Calcolo "M. Picone", IAC-CNR, Viale del Policlinico, 137, 00161, Roma
3.
Istituto per le Applicazioni del Calcolo "M. Picone", IAC-CNR, Viale del Policlinico 137, 00161 Roma
4.
Dipartimento di Matematica, Università di Roma "La Sapienza", Piazzale Aldo Moro, 5, 00185, Roma

Received: May 31, 2006

Revised: October 31, 2006

Published: February 2007

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Abstract

We consider a hyperbolic conservation law with discontinuous flux. Such a partial differential equation arises in different applications, in particular we are motivated by a model of traffic flow. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the corresponding weak entropic solutions.

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Mathematics Subject Classification: Primary: 35L50, 35L65, 90B20; Secondary: 76S05.

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