Global well-posedness and asymptotic behavior of $ BV $ solutions to a system of balance laws arising in traffic flow

Tong Li; Nitesh Mathur; Tong Li; Nitesh Mathur

doi:10.3934/nhm.2023025

Networks and Heterogeneous Media

2023, Volume 18, Issue 2: 581-600. doi: 10.3934/nhm.2023025

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Research article

Global well-posedness and asymptotic behavior of $ BV $ solutions to a system of balance laws arising in traffic flow

Tong Li ^,,
Nitesh Mathur

Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA

Received: 15 December 2022 Revised: 27 January 2023 Accepted: 27 January 2023 Published: 01 February 2023

We establish global well-posedness and asymptotic behavior of $ BV $ solutions to a system of balance laws modeling traffic flow with nonconcave fundamental diagram. We prove the results by finding a convex entropy-entropy flux pair and verifying the Kawashima condition, the sub-characteristic condition, and the partial dissipative inequality in the framework of Dafermos. This problem is of specific interest since nonconcave fundamental diagrams arise naturally in traffic flow.
- hyperbolic balance laws,
- global $ BV $ solution,
- entropy-entropy flux pairs,
- cauchy problem,
- traffic flow,
- relaxation,
- nonconcave fundamental diagram
Citation: Tong Li, Nitesh Mathur. Global well-posedness and asymptotic behavior of $ BV $ solutions to a system of balance laws arising in traffic flow[J]. Networks and Heterogeneous Media, 2023, 18(2): 581-600. doi: 10.3934/nhm.2023025

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Abstract

We establish global well-posedness and asymptotic behavior of $ BV $ solutions to a system of balance laws modeling traffic flow with nonconcave fundamental diagram. We prove the results by finding a convex entropy-entropy flux pair and verifying the Kawashima condition, the sub-characteristic condition, and the partial dissipative inequality in the framework of Dafermos. This problem is of specific interest since nonconcave fundamental diagrams arise naturally in traffic flow.

References

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