关于δ初值的Chaplygin 压交通流AR 模型的Riemann问题

数学物理学报 ›› 2014, Vol. 34 ›› Issue (6): 1353-1371.

关于δ初值的Chaplygin 压交通流AR 模型的Riemann问题

邵志强

福州大学数学与计算机科学学院福州 350116

收稿日期:2013-05-28 修回日期:2014-10-27 出版日期:2014-12-25 发布日期:2014-12-25
基金资助:
福建省自然科学基金(2012J01006)资助.

The Riemann Problem with Delta Initial Data for the Aw-Rascle Traffic Model with Chaplygin Pressure

SHAO Zhi-Qiang

College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116

Received:2013-05-28 Revised:2014-10-27 Online:2014-12-25 Published:2014-12-25
Supported by:
福建省自然科学基金(2012J01006)资助.

摘要/Abstract

摘要：

研究Chaplygin 压交通流AR 模型初值含Dirac δ 函数的Riemann问题. 在广义Rankine-Hugoniot条件和熵条件下, 构造性地获得了包含δ 激波的整体广义解, 明确地显示出四种不同的结构. 结果表明, 在Riemann初值这里构造的扰动下, Riemann解是稳定的.

关键词: Chaplygin 压交通流AR 模型, Riemann问题, 广义Rankine-Hugoniot 条件, &delta, 激波, 熵条件

Abstract:

In this paper, we study the Riemann problem with the initial data containing the Dirac delta function for the Aw-Rascle traffic model with Chaplygin pressure. Under the generalized Rankine-Hugoniot relation and the entropy condition, we constructively obtain the global existence and uniqueness of generalized solutions including delta shock waves that explicitly exhibit four kinds of different structures. Moreover, it can be found that the solutions constructed here are stable for some perturbations of the initial data.

Key words: Aw-Rascle traffic model, Chaplygin pressure, Riemann problem, Generalized Rankine-Hugoniot relation, Delta shock wave, Entropy condition

中图分类号:

35L65

邵志强. 关于δ初值的Chaplygin 压交通流AR 模型的Riemann问题[J]. 数学物理学报, 2014, 34(6): 1353-1371.

SHAO Zhi-Qiang. The Riemann Problem with Delta Initial Data for the Aw-Rascle Traffic Model with Chaplygin Pressure[J]. Acta mathematica scientia,Series A, 2014, 34(6): 1353-1371.

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