J. Korean Math. Soc. 2020; 57(4): 987-1004
Online first article January 9, 2020 Printed July 1, 2020
https://doi.org/10.4134/JKMS.j190488
Copyright © The Korean Mathematical Society.
Yongki Lee
Georgia Southern University
Motivated by the traffic flow model with Arrhenius look-ahead relaxation dynamics introduced in \cite{SK06}, this paper proposes a traffic flow model with look ahead relaxation-behind intensification by inserting look behind intensification dynamics to the flux. Finite time shock formation conditions in the proposed model with various types of interaction potentials are identified. Several numerical experiments are performed in order to demonstrate the performance of the modified model. It is observed that, comparing to other well-known macroscopic traffic flow models, the model equipped with look ahead relaxation-behind intensification has both enhanced dispersive and smoothing effects
Keywords: Nonlocal conservation law, shock formation, traffic flow, global flux
MSC numbers: Primary 35L65; Secondary 35L67
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