论文标题
由自动车辆交通流量模型引起的非线性热方程
A Nonlinear Heat Equation Arising from Automated-Vehicle Traffic Flow Models
论文作者
论文摘要
在本文中，研究了一种新的非线性热方程，该方程是自动车辆集体行为的模型。通过引入需要某些类似熵状条件的弱解的适当概念来研究该方程的溶液的性能。为了获得非线性热方程溶液的近似值，提出了一个新的保守的一阶有限差差方案，该方案尊重相应的熵条件，并提供了弱解决方案与数值方案之间的某些联系。最后，提供了交通模拟方案和与Lighthill-Witham-Richards（LWR）模型的比较，说明了使用自动车辆的好处。
In this paper, a new nonlinear heat equation is studied that arises as a model of the collective behavior of automated vehicles. The properties of the solutions of this equation are studied by introducing the appropriate notion of a weak solution that requires certain entropy-like conditions. To obtain an approximation of the solution of the nonlinear heat equation, a new conservative first-order finite difference scheme is proposed that respects the corresponding entropy conditions, and certain links between the weak solution and the numerical scheme are provided. Finally, a traffic simulation scenario and a comparison with the Lighthill-Witham-Richards (LWR) model are provided, illustrating the benefits of the use of automated vehicles.
