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