Conservation laws with discontinuous flux

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March 2007, 2(1): 159-179. doi: 10.3934/nhm.2007.2.159

Conservation laws with discontinuous flux

Mauro Garavello ^1, , Roberto Natalini ^2, , Benedetto Piccoli ^3, and Andrea Terracina ^4,

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, Italy

Received June 2006 Revised November 2006 Published December 2006

Abstract
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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.

Keywords: discontinuous flux, traffic flow, Conservation laws, Riemann Solvers, front tracking.

Mathematics Subject Classification: Primary: 35L50, 35L65, 90B20; Secondary: 76S0.

Citation: Mauro Garavello, Roberto Natalini, Benedetto Piccoli, Andrea Terracina. Conservation laws with discontinuous flux. Networks & Heterogeneous Media, 2007, 2 (1) : 159-179. doi: 10.3934/nhm.2007.2.159

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