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Displaying items by tag: finite time wave breakdown

 

Yongki Lee, and Changhui Tan

Communications in Mathematical Sciences, Volume 20, No. 4, pp. 1151-1172 (2022).


Abstract

We study a Lighthill-Whitham-Richards (LWR) type traffic flow model, with a nonlocal look-ahead interaction that has a slow-down effect depending on the traffic ahead. We show a sharp critical threshold condition on the initial data that distinguishes global smooth solutions and finite- time wave breakdown. It is well-known that the LWR model leads to a finite-time shock formation, representing the creation of traffic jams, for generic smooth initial data with finite mass. Our result shows that the nonlocal slowdown effect can help to prevent shock formations, for a class of subcritical initial data.


   doi:10.4310/CMS.2022.v20.n4.a9
 Download the Published Version
 This work is supported by NSF grants DMS #1853001 and DMS #2108264
 This work is supported by a UofSC VPR ASPIRE I grant
Published in Research