论文标题
一类非本地交通流模型的急剧关键阈值
Sharp critical thresholds for a class of nonlocal traffic flow models
论文作者
论文摘要
我们研究具有非本地外观相互作用的一类交通流模型。解决方案的全球规律性取决于初始数据。我们获得了尖锐的临界阈值条件，将初始数据区分为三分法：亚临界初始条件导致全球平滑解决方案，而两种类型的超临界初始条件会导致两种有限的时间冲击形成。非平凡的亚临界初始数据的存在表明，非局部外观相互作用可以帮助避免冲击形成，从而阻止产生交通拥堵。
We study a class of traffic flow models with nonlocal look-ahead interactions. The global regularity of solutions depend on the initial data. We obtain sharp critical threshold conditions that distinguish the initial data into a trichotomy: subcritical initial conditions lead to global smooth solutions, while two types of supercritical initial conditions lead to two kinds of finite time shock formations. The existence of non-trivial subcritical initial data indicates that the nonlocal look-ahead interactions can help avoid shock formations, and hence prevent the creation of traffic jams.
