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

doi:10.1007/s10483-015-1915-6

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (3): 353-364.doi: https://doi.org/10.1007/s10483-015-1915-6

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

Wancheng SHENG¹, Ying ZENG^1,2

1. Department of Mathematics, Shanghai University, Shanghai 200444, China;
2. Department of Mathematics and Physics, Quzhou University, Quzhou 324000, Zhejiang Province, China

收稿日期:2014-04-14 修回日期:2014-07-17 出版日期:2015-03-01 发布日期:2015-03-01
通讯作者: Wancheng SHENG E-mail:mathwcsheng@shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11371240), the Scientific Research Innovation Project of Shanghai Municipal Education Commission (No. 11ZZ84), and the grant of “The First-Class Discipline of Universities in Shanghai”

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

Wancheng SHENG¹, Ying ZENG^1,2

1. Department of Mathematics, Shanghai University, Shanghai 200444, China;
2. Department of Mathematics and Physics, Quzhou University, Quzhou 324000, Zhejiang Province, China

Received:2014-04-14 Revised:2014-07-17 Online:2015-03-01 Published:2015-03-01
Contact: Wancheng SHENG E-mail:mathwcsheng@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11371240), the Scientific Research Innovation Project of Shanghai Municipal Education Commission (No. 11ZZ84), and the grant of “The First-Class Discipline of Universities in Shanghai”

摘要/Abstract

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 gen- eralized 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.

关键词: -entropy condition, Delta initial datum, generalized &delta, Chaplygin gas, generalized Rankine-Hugoniot relation, Riemann problem for Aw-Rascle model

Abstract: 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 gen- eralized 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.

Key words: generalized Rankine-Hugoniot relation, Riemann problem for Aw-Rascle model, Chaplygin gas, generalized δ-entropy condition, Delta initial datum

中图分类号:

O175.27

O175.29

O351.3

引用本文

Wancheng SHENG;Ying ZENG. Generalized δ-entropy condition to Riemann solution for Chaplygin gas in traffic flow[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 353-364.

Wancheng SHENG;Ying ZENG. Generalized δ-entropy condition to Riemann solution for Chaplygin gas in traffic flow[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 353-364.

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链接本文: https://www.amm.shu.edu.cn/CN/10.1007/s10483-015-1915-6

https://www.amm.shu.edu.cn/CN/Y2015/V36/I3/353

参考文献

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[1]	陈荣三. 大密度比和大压力比可压缩流的数值计算[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(5): 673-682 .
[2]	刘亚成;徐润章;于涛. Wave equations and reaction-diffusion equations with several nonlinear source terms[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(9): 1209-1218 .
[3]	孙文华;盛万成. Two-dimensional non-selfsimilar initial value problem for adhesion particle dynamics[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(9): 1191-1198 .
[4]	舒级;张健. On a class of quasilinear Schrödinger equations[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(7): 981-986 .
[5]	刘法贵. Life-span of classical solutions for one-dimensional hydromagnetic flow[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(4): 511-520 .
[6]	刘法贵;孔德兴. GLOBAL EXISTENCE AND BLOW-UP PHENOMENA OF CLASSICAL SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(6): 703-713.
[7]	刘安平;何猛省. OSCILLATORY PROPERTIES OF THE SOLUTIONS OF NONLINEAR DELAY HYPERBOLIC DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(6): 678-685.
[8]	同小军;同登科;陈绵云. THE MEAN VALUE THEOREM AND CONVERSE THEOREM OF ONE CLASS THE FOURTH-ORDER PARTIAL DIFFERENTIAL EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(6): 717-723.
[9]	熊岳山;韦永康. THE ANALYTICAL SOLUTION FOR SEDIMENT REACTION AND DIFFUSION EQUATION WITH GENERALIZED INITIAL-BOUNDARY CONDITIONS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(4): 404-408.
[10]	曹镇潮;王碧祥. ABOUT A CONDITION FOR BLOW UP OF SOLUTIONS OF CAUCHY PROBLEM FOR A WAVE EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(9): 1010-1013.