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Vanishing Viscosity for Traffic on Networks with Degenerate Diffusivity

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Abstract

We consider the vanishing viscosity approximation of the traffic model LWR with degenerate diffusivity on a networks composed by a single junction with n incoming and m outgoing roads. We prove that the solution of the parabolic approximation exists and, as the viscosity vanishes, the solution of the parabolic problem converges to a solution of the original problem.

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Authors and Affiliations

  1. Dipartimento di Meccanica Matematica e Management, Politecnico di Bari, via E. Orabona 4, 70125, Bari, Italy

    Giuseppe Maria Coclite

  2. Dipartimento di Matematica, Università di Bari, via E. Orabona 4, 70125, Bari, Italy

    Lorenzo di Ruvo

Authors
  1. Giuseppe Maria Coclite
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  2. Lorenzo di Ruvo
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Correspondence to Giuseppe Maria Coclite.

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The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Coclite, G.M., di Ruvo, L. Vanishing Viscosity for Traffic on Networks with Degenerate Diffusivity. Mediterr. J. Math. 16, 110 (2019). https://doi.org/10.1007/s00009-019-1391-1

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  • DOI: https://doi.org/10.1007/s00009-019-1391-1

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