论文标题
耗散AW-RASCLE系统的硬充血极限
Hard congestion limit of the dissipative Aw-Rascle system
论文作者
论文摘要
在这项研究中，我们分析了著名的AW-RASCLE系统，其中实际速度和所需速度（偏移函数）之间的差异是密度奇异函数的梯度。这会导致动量方程式中的耗散，当密度为零时消失。所得的PDE系统可用于在一个维度上对流量或悬架流进行建模，并考虑到最大填料约束。在证明了平滑解决方案的全球存在之后，我们研究了所谓的“硬拥塞限制”，并显示了解决方案向混合自由释放系统的弱解决方案的范围融合。在悬浮流的背景下，该极限可以看作是从润滑力驱动的悬架状态的过渡，朝着颗粒状状态，由谷物之间的接触驱动。
In this study, we analyse the famous Aw-Rascle system in which the difference between the actual and the desired velocities (the offset function) is a gradient of a singular function of the density. This leads to a dissipation in the momentum equation which vanishes when the density is zero. The resulting system of PDEs can be used to model traffic or suspension flows in one dimension with the maximal packing constraint taken into account. After proving the global existence of smooth solutions, we study the so-called "hard congestion limit", and show the convergence of a subsequence of solutions towards a weak solution of an hybrid freecongested system. In the context of suspension flows, this limit can be seen as the transition from a suspension regime, driven by lubrication forces, towards a granular regime, driven by the contact between the grains.
