Moving bottlenecks in road traffic represent an interesting mathematical problem, which can be modeled via coupled PDE-ODE systems. We consider the case of a scalar conservation law modeling the evolution of vehicular traffic and an ODE with discontinuous right-hand side for the bottleneck introduced in [M.L. Delle Monache and P. Goatin, J. Diff. Eqs., 257(11):4015–4029, 2014]. The bottleneck usually corresponds to a slow-moving vehicle influencing the bulk traffic flow via a moving flux pointwise constraint. The definition of solutions requires a special entropy condition selecting non-classical shocks and we prove existence of such solutions for initial data with bounded variation. Approximate solutions are constructed via the wave-front tracking method and their limit are solutions of the Cauchy problem PDE-ODE.

中文翻译：

---

关于与移动瓶颈相结合的守恒定律的熵解

道路交通中的移动瓶颈代表了一个有趣的数学问题，可以通过耦合 PDE-ODE 系统进行建模。我们考虑了一个标量守恒定律的情况，它对车辆交通的演变进行建模，以及一个 ODE 的右侧不连续，用于在 [ML Delle Monache 和 P. Goatin，J. Diff. 方程式, 257(11):4015–4029, 2014]。瓶颈通常对应于通过移动通量逐点约束影响大量交通流的缓慢移动的车辆。解的定义需要一个特殊的熵条件来选择非经典冲击，我们证明了对于有界变化的初始数据存在这样的解。近似解是通过波前跟踪方法构建的，它们的极限是柯西问题 PDE-ODE 的解。