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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics

Pages: 323 - 339, Volume 35, Issue 1, January 2015      doi:10.3934/dcds.2015.35.323

 
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Yongki Lee - Department of Mathematics, Iowa State University, Ames, IA 50011, United States (email)
Hailiang Liu - Department of Mathematics, Iowa State University, Ames, IA 50011, United States (email)

Abstract: We investigate a class of nonlocal conservation laws with the nonlinear advection coupling both local and nonlocal mechanism, which arises in several applications such as the collective motion of cells and traffic flows. It is proved that the $C^1$ solution regularity of this class of conservation laws will persist at least for a short time. This persistency may continue as long as the solution gradient remains bounded. Based on this result, we further identify sub-thresholds for finite time shock formation in traffic flow models with Arrhenius look-ahead dynamics.

Keywords:  Nonlocal conservation laws, well-posedness, shock formation, critical threshold, traffic flows.
Mathematics Subject Classification:  Primary: 35L65; Secondary: 35L67.

Received: January 2014;      Revised: February 2014;      Available Online: August 2014.

 References