A Hamilton-Jacobi approach to junction problems and application to traffic flows
A Hamilton-Jacobi approach to junction problems and application to traffic flows
复制标题
解决路口问题的汉密尔顿-雅可比方法及其在交通流中的应用
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
H. Zidani
中科院分区：
文献类型：
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作者：
C. Imbert;R. Monneau;H. Zidani
本文研究了一阶Hamilton-Jacobi方程组在一个“结点”上的一个典型情形，即有限个半直线的并点有唯一的公共点。主要结果是一个比较原则。我们还证明了解的存在性和稳定性。两个具有挑战性的困难是奇异几何的域和不连续的哈密尔顿。就间断哈密顿量而言，这些结果似乎是新的。它们被应用于交通流中出现的一些模型的研究。本文中开发的技术为分析此类问题提供了新的强有力的工具。
This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a 'junction', that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison principle. We also prove existence and stability of solutions. The two challenging difficulties are the singular geometry of the domain and the discontinuity of the Hamiltonian. As far as discontinuous Hamiltonians are concerned, these results seem to be new. They are applied to the study of some models arising in traffic flows. The techniques developed in the present article provide new powerful tools for the analysis of such problems.