标题： 交通流动力学模型的BGK近似 显示英文标题

标题： The BGK approximation of kinetic models for traffic

摘要： 我们研究用于车辆交通流的空间非均匀动力学模型。 经典的表述，例如BGK方程，在交通的拥挤状态下会导致无条件不稳定的解。 我们通过推导BGK型方程的修改公式来解决这个问题。 新的动力学模型能够再现交通流中条件稳定的非平衡现象。 特别是，停止和前进波作为有限密度区域中发生的有限向后传播信号出现，此时模型是不稳定的。 这里引入的BGK型模型还提供了微观跟随前车模型和宏观Aw-Rascle和Zhang模型之间的介观描述。 显示英文摘要

摘要： We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by deriving a modified formulation of the BGK-type equation. The new kinetic model allows to reproduce conditionally stable non-equilibrium phenomena in traffic flow. In particular, stop and go waves appear as bounded backward propagating signals occurring in bounded regimes of the density where the model is unstable. The BGK-type model introduced here also offers the mesoscopic description between the microscopic follow-the-leader model and the macroscopic Aw-Rascle and Zhang model.