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Research Article | Open Access

Global well-posedness and asymptotic behavior of B V 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
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Abstract

We establish global well-posedness and asymptotic behavior of B V 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.

Keywords

hyperbolic balance lawsglobal BV solutionentropy-entropy flux pairscauchy problemtraffic flowrelaxationnonconcave fundamental diagram

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Networks and Heterogeneous Media
Volume 18 Issue 2,
June 2023
Pages 581-600
DOI: 10.3934/nhm.2023025

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Cite this article:
Li T, Mathur N. Global well-posedness and asymptotic behavior of B V solutions to a system of balance laws arising in traffic flow. Networks and Heterogeneous Media, 2023, 18(2): 581-600. https://doi.org/10.3934/nhm.2023025

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Received: 15 December 2022
Revised: 27 January 2023
Accepted: 27 January 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)