Thomas Hamori and Changhui Tan
Nonlinear Analysis: Real World Applications, Volume 73, 103899, (2023).
Abstract
We study a class of traffic flow models with nonlocal look-ahead interactions. The global regularity of solutions depend on the initial data. We obtain sharp critical threshold conditions that distinguish the initial data into a trichotomy: subcritical initial conditions lead to global smooth solutions, while two types of supercritical initial conditions lead to two kinds of finite time shock formations. The existence of non-trivial subcritical initial data indicates that the nonlocal look-ahead interactions can help avoid shock formations, and hence prevent the creation of traffic jams.
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doi:10.1016/j.nonrwa.2023.103899 |
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This work is supported by NSF grant DMS #1853001 and DMS #2108264 |
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This work is supported by a UofSC VPR ASPIRE I grant |