A NOTE ON THE INTERACTIONS OF ELEMENTARY WAVES FOR THE AR TRAFFIC FLOW MODEL WITHOUT VACUUM

doi:10.1016/S0252-9602(11)60336-6

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (4): 1503-1512.doi: 10.1016/S0252-9602(11)60336-6

A NOTE ON THE INTERACTIONS OF ELEMENTARY WAVES FOR THE AR TRAFFIC FLOW MODEL WITHOUT VACUUM

孙梅娜

Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China School of Mathematical and Information, Ludong University, Yantai 264025, China

收稿日期:2009-03-16 修回日期:2011-01-22 出版日期:2011-07-20 发布日期:2011-07-20
基金资助:
Sponsored by National Natural Science Foundation of China (10901077); China Postdoctoral Science Foundation (201003504; 20090451089) and Shandong Provincial Doctoral Foundation (BS2010SF006).

A NOTE ON THE INTERACTIONS OF ELEMENTARY WAVES FOR THE AR TRAFFIC FLOW MODEL WITHOUT VACUUM

SUN Mei-Na

Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China School of Mathematical and Information, Ludong University, Yantai 264025, China

Received:2009-03-16 Revised:2011-01-22 Online:2011-07-20 Published:2011-07-20
Supported by:
Sponsored by National Natural Science Foundation of China (10901077); China Postdoctoral Science Foundation (201003504; 20090451089) and Shandong Provincial Doctoral Foundation (BS2010SF006).

摘要/Abstract

摘要：

In this note, we consider the interactions of elementary waves for the traffic flow model proposed by Aw and Rascle when the vacuum is not involved. The solutions are obtained constructively and globally when the initial data consist of three pieces of constant states. Furthermore, it can be found that the Riemann solutions are stable with respect to such small perturbations of the initial data in this particular situation by investigating the limits of the solutions as the perturbed parameter " goes to zero.

关键词: interaction of elementary wave, Aw-Rascle model, Riemann problem, traffic flow, hyperbolic conservation laws

Abstract:

Key words: interaction of elementary wave, Aw-Rascle model, Riemann problem, traffic flow, hyperbolic conservation laws

中图分类号:

35L65

孙梅娜. A NOTE ON THE INTERACTIONS OF ELEMENTARY WAVES FOR THE AR TRAFFIC FLOW MODEL WITHOUT VACUUM[J]. 数学物理学报(英文版), 2011, 31(4): 1503-1512.

SUN Mei-Na. A NOTE ON THE INTERACTIONS OF ELEMENTARY WAVES FOR THE AR TRAFFIC FLOW MODEL WITHOUT VACUUM[J]. Acta mathematica scientia,Series B, 2011, 31(4): 1503-1512.

参考文献

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[6] Greenberg J M, Klar A, Rascle M. Congestion on multilane highways. SIAM J Appl Math, 2003, 63: 818–833

[7] Herty M, Rascle M. Coupling conditions for a class of second-order models for traffic flow. SIAM J Math Anal, 2006, 38: 595–616

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[9] Moutari S, Rascle M. A hybrid Lagrangian model based on the Aw-Rascle traffic flow model. SIAM J Appl Math, 2007, 68: 413–436

[10] Shen C, Sun M. Formation of delta shocks and vacuum states in the vanishing pressure limit of Riemann solutions to the perturbed Aw-Rascle model. J Differ Equ, 2010, 249: 3024–3051

[11] Sun M. Interactions of elementary waves for the Aw-Rascle model. SIAM J Appl Math, 2009, 69: 1542–1558

[12] Smoller J. Shock Waves and Reaction-Diffusion Equations. New York: Springer-Verlag, 1994

[13] Chang T, Hsiao L. The Riemann Problem and Interaction of Waves in Gas Dynamics. Pitman Monographs and Surveys in Pure and Applied Mathematics 41. New York: Longman Scientific and Technical, 1989

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[15] Shen C. Wave interactions and stability of the Riemann solutions for the chromatography equations. J Math Anal Appl, 2010, 365: 609–618

A NOTE ON THE INTERACTIONS OF ELEMENTARY WAVES FOR THE AR TRAFFIC FLOW MODEL WITHOUT VACUUM

A NOTE ON THE INTERACTIONS OF ELEMENTARY WAVES FOR THE AR TRAFFIC FLOW MODEL WITHOUT VACUUM

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