Thresholds for shock formation in traffic flow models with nonlocal-concave-convex flux

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Lee, Yongki¹ 

[1] Georgia Southern Univ, Dept Math Sci, Statesboro, GA 30458 USA

关键词: Nonlocal conservation law;    Traffic flow;    Shock formation;    Blow up;    Critical threshold;    Nonconcave flux;    Look-ahead dynamics;   

DOI  :  10.1016/j.jde.2018.07.048

来源: Elsevier

【 摘 要 】

We identify sub-thresholds for finite time shock formation in a class of non-local conservation law with concavity changing flux. From a class of non-local conservation laws, the Riccati-type ODE system that governs a solution's gradient is obtained. The changes in concavity of the flux function correspond to the sign changes in the leading coefficient functions of the ODE system. We identify the blow up condition of this structurally generalized Riccati-type ODE. The method is illustrated via the traffic flow models with nonlocal-concave-convex flux. The techniques and ideas developed in this paper is applicable to a large class of non-local conservation laws. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free