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A Fluidodynamic Model for Traffic in a Road Network

In: Traffic and Granular Flow’05

Author

Listed:
  • Mauro Garavello

    (Università di Milano Bicocca, Dipartimento di Matematica e Applicazioni)

  • Benedetto Piccoli

    (Istituto per le Applicazioni del Calcolo “M. Picone”)

Abstract

Summary This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from the conservation of the number of cars, defined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence of solutions to the Cauchy problem and we show that the Lipschitz continuous dependence by initial data does not hold. Our method is based on wave front tracking approach, see [4].

Suggested Citation

  • Mauro Garavello & Benedetto Piccoli, 2007. "A Fluidodynamic Model for Traffic in a Road Network," Springer Books, in: Andreas Schadschneider & Thorsten Pöschel & Reinhart Kühne & Michael Schreckenberg & Dietrich E. Wol (ed.), Traffic and Granular Flow’05, pages 383-392, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-47641-2_34
    DOI: 10.1007/978-3-540-47641-2_34
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