SIAM Journal on Applied Mathematics, Volume 80, Issue 6, Page 2319-2337, January 2020.
The meaning of weak solutions of a nonconservative hyperbolic system with discontinuous coefficients modeling traffic flows involving hysteresis is defined. An upwinding approximation scheme for the model is shown to be total variation diminishing. Vehicles' speeds and drivers' hysteresis states satisfy maximum and minimum principles. The limit of a convergent subsequence generated by the approximation scheme is shown to be a weak solution of the model if it is piecewise $C^1$, establishing the existence of such solutions.

中文翻译：

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滞后交通模型的解的存在性与计算

SIAM应用数学杂志，第80卷，第6期，第2319-2337页，2020年1月
。定义了非保守双曲系统的弱解的含义，该系统具有不连续系数来建模涉及滞后的交通流。该模型的迎风近似方案显示出总变化减小。车辆的速度和驾驶员的磁滞状态满足最大和最小原则。由近似方案产生的收敛子序列的极限被证明是该模型的弱解，如果它是分段$ C ^ 1 $，则证明了这种解的存在。