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Networks and Heterogeneous Media

2011, Volume 6, Issue 4: 681-694. doi: 10.3934/nhm.2011.6.681
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Shock formation in a traffic flow model with Arrhenius look-ahead dynamics

  • 1.
    Department of Mathematics, University of Iowa, Iowa City, IA 52242
  • 2.
    Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419
  • Received: 01 January 2011 Revised: 01 October 2011

  • Primary: 35B44, 35L65, 35L67, 35Q35, 76L05, 90B20.

  • We consider a nonlocal traffic flow model with Arrhenius look-ahead dynamics. We provide a complete local theory and give the blowup alternative of solutions to the conservation law with a nonlocal flux. We show that the finite time blowup of solutions must occur at the level of the first order derivative of the solution. Furthermore, we prove that finite time singularities do occur for several types of physical initial data by analyzing the solutions on different characteristic lines. These results are new and are consistent with the blowups observed in previous numerical simulations on the nonlocal traffic flow model [6].

    Citation: Dong Li, Tong Li. Shock formation in a traffic flow model with Arrhenius look-ahead dynamics[J]. Networks and Heterogeneous Media, 2011, 6(4): 681-694. doi: 10.3934/nhm.2011.6.681

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  • We consider a nonlocal traffic flow model with Arrhenius look-ahead dynamics. We provide a complete local theory and give the blowup alternative of solutions to the conservation law with a nonlocal flux. We show that the finite time blowup of solutions must occur at the level of the first order derivative of the solution. Furthermore, we prove that finite time singularities do occur for several types of physical initial data by analyzing the solutions on different characteristic lines. These results are new and are consistent with the blowups observed in previous numerical simulations on the nonlocal traffic flow model [6].


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