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Networks and Heterogeneous Media (NHM)
 

Conservation laws with discontinuous flux

Pages: 159 - 179, Volume 2, Issue 1, March 2007      doi:10.3934/nhm.2007.2.159

 
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Mauro Garavello - Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via R. Cozzi 53 - Edificio U5, 20125 - Milano, Italy (email)
Roberto Natalini - Istituto per le Applicazioni del Calcolo "M. Picone", IAC-CNR, Viale del Policlinico, 137, 00161, Roma, Italy (email)
Benedetto Piccoli - Istituto per le Applicazioni del Calcolo "M. Picone", IAC-CNR, Viale del Policlinico 137, 00161 Roma, Italy (email)
Andrea Terracina - Dipartimento di Matematica, Università di Roma "La Sapienza", Piazzale Aldo Moro, 5, 00185, Roma, Italy (email)

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.

Keywords:  Conservation laws, discontinuous flux, Riemann Solvers, front tracking, traffic flow
Mathematics Subject Classification:  Primary: 35L50, 35L65, 90B20; Secondary: 76S05.

Received: June 2006;      Revised: November 2006;      Available Online: December 2006.