由自动车辆交通流模型产生的非线性Heat Equation
A Nonlinear Heat Equation Arising from Automated-Vehicle Traffic Flow Models
摘要：
在本文中，一个新的非线性热方程进行了研究，出现作为自动驾驶汽车的集体行为的模型。通过引入适当的弱解的概念，研究了该方程解的性质，该解需要一定的类熵条件。为了得到非线性热方程解的近似解，提出了一种新的守恒一阶差分格式，该格式满足相应的熵条件，并给出了弱解与数值格式之间的某些联系.最后，提供了一个交通模拟场景和与Lighthill-Witham-Richards（LWR）模型的比较，说明了使用自动驾驶汽车的好处。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
