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Semidiscrete Shocks for the Full Velocity Difference Model

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Abstract

In this paper, we consider the full velocity difference model for traffic flow and we study the existence and uniqueness of traveling wave solutions. First, using the monotony of the car’s interdistance, we derive necessary conditions for the existence of such solutions. Then, in the framework of viscosity solutions, we construct a traveling wave solution by considering an approximate non-local Hamilton–Jacobi equation on a bounded domain. This traveling wave solution can be interpreted as a phase transition between a congested state and a free-flow one.

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Funding

This research was funded, partially, by l’Agence Nationale de la Recherche (ANR), project ANR-22-CE40-0010. For the purpose of open access, the author has applied a CC-BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission.

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Authors and Affiliations

  1. Department of Computer Science and Mathematics, Lebanese American University, Byblos Campus, P.O. Box 36, Byblos, Lebanon

    Nader El Khatib & Mamdouh Zaydan

  2. INSA Rouen Normandie, Normandie Univ, LMI UR 3226, 7600, Rouen, France

    Nicolas Forcadel

Authors
  1. Nader El Khatib
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  2. Nicolas Forcadel
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  3. Mamdouh Zaydan
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Correspondence to Mamdouh Zaydan.

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El Khatib, N., Forcadel, N. & Zaydan, M. Semidiscrete Shocks for the Full Velocity Difference Model. Appl Math Optim 88, 56 (2023). https://doi.org/10.1007/s00245-023-10029-x

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