Moving Bottlenecks in Car Traffic Flow: A PDE-ODE Coupled Model

We study a model of vehicular traffic flow, represented by a coupled system formed by a scalar conservation law, describing the evolution of cars density, and an ODE, whose solution is the position of a moving bottleneck, i.e., a slower vehicle moving inside the cars' flow. A fractional step approach is used to approximate the coupled model, and convergence is proved by compactness arguments. Finally, the limit of such an approximating sequence is proved to solve the original PDE-ODE model.