Generalized δ-entropy condition to Riemann solution for Chaplygin gas in traffic flow

被引：0
作者：
Wancheng Sheng
Ying Zeng
机构：
[1] Shanghai University,Department of Mathematics
[2] Quzhou University,Department of Mathematics and Physics
来源：
Applied Mathematics and Mechanics | 2015年 / 36卷
关键词：
generalized ; -entropy condition; Riemann problem for Aw-Rascle model; generalized Rankine-Hugoniot relation; Delta initial datum; Chaplygin gas; O175.27; O175.29; O351.3; 35L65; 35L67; 35B30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The Riemann problem for the Aw-Rascle model in the traffic flow with the Delta initial data for the Chaplygin gas is studied. The solutions are constructed globally under the generalized Rankine-Hugoniot relations, the δ-entropy conditions, and the generalized δ-entropy conditions. A new Delta wave, which is called a primary Delta wave, is defined in some solutions. The primary Delta wave satisfies the generalized Rankine-Hugoniot relations and the generalized δ-entropy conditions. It generates initially from the Delta initial data, which either evaluates a Delta wave, whose weight becomes stronger and stronger, or disappears at a finite time.
引用
收藏
页码：353 / 364
页数：11
相关论文
共 18 条
  • [1] Lighthill M J(1955)On kinematic waves. II: a theory of traffic flow on long crowded roads Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 229A 317-345
  • [2] Whitham G B(1956)Shock waves on the highway Operations Research 4 42-51
  • [3] Richards P(2000)Resurrection of second order models of traffic flow Journal on Applied Mathematics 60 916-938
  • [4] Aw A(1995)Requiem for second-order fluid approximation of traffic flow Transportation Research: Part B 29 277-286
  • [5] Rascle M(2002)Hyperbolic conservation laws in traffic flow Journal on Applied Mathematics 63 708-721
  • [6] Daganzo C F(2009)Interactions of elementary waves for the AW-Rascle model Journal on Applied Mathematics 69 1542-1558
  • [7] Colombo R M(1999)The Riemann problem for the transportation equations in gas dynamics Memoirs of the American Mathematical Society 137 1-77
  • [8] Sun M N(2010)The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system Communications on Pure and Applied Analysis 9 431-458
  • [9] Sheng W C(2012)The Riemann problem with Delta initial data for the one-dimensional Chaplygin gas equations Acta Mathematica Scientia 32 825-841
  • [10] Zhang T(2013)The Aw-Rascle traffic model with Chaplygin pressure Journal of Mathematical Analysis and Applications 401 379-387
12