Thresholds for shock formation in traffic flow models with nonlocal-concave-convex flux
Thresholds for shock formation in traffic flow models with nonlocal-concave-convex flux
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具有非局部凹凸通量的交通流模型中冲击形成的阈值
DOI：
10.1016/j.jde.2018.07.048
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发表时间：
2019
影响因子：
2.4
通讯作者：
Yongki Lee
中科院分区：
文献类型：
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作者：
Yongki Lee
我们确定了一类非定域守恒律方程中有限时间激波形成的亚阈值。从一类非局部守恒律出发，得到了控制解的梯度的Riccati型常微分方程组。通量函数的符号变化对应于常微分方程系统的前导系数函数的符号变化。我们确定了这个结构广义Riccati型常微分方程的爆破条件。通过非局部凹凸流量的交通流模型说明了该方法。本文的方法和思想适用于一类非局部守恒律。
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.