Shock formation in a traffic flow model with Arrhenius look-ahead dynamics

Pages: 681 - 694, Volume 6, Issue 4, December 2011

doi:10.3934/nhm.2011.6.681       Abstract        References        Full Text (396.8K)       Related Articles

Dong Li - Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States (email)
Tong Li - Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States (email)

Abstract: 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].

Keywords:  Traffic flow, Arrhenius look-ahead dynamics, nonlocal flux, shock waves, blowup criteria.
Mathematics Subject Classification:  Primary: 35B44, 35L65, 35L67, 35Q35, 76L05, 90B20.

Received: January 2011;      Revised: October 2011;      Published: December 2011.

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