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

2013/04/04 by Yongki Lee, Hailiang Liu, Lee, Yongki +1
Engineering · Mathematics · #35L65(Primary) #35L67(Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Mathematical Biology Tumor Growth #Traffic control and management

paper · pdf · doi:10.48550/arxiv.1304.1562

openalex publication_date 2013/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 C¹ 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.

Citations

• Wave breaking for nonlinear nonlocal shallow water equations

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