AAM  >> Vol. 2 No. 3 (August 2013)

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

  • 全文下载: PDF(260KB) HTML    PP.114-126   DOI: 10.12677/AAM.2013.23015  
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Aw-Rascle交通模型广义Rankine-Hugoniot条件Delta-激波线性退化熵条件 Aw-Rascle Traffic Model; Generalized Rankine-Hugoniot Relation; Delta Shock Wave; Linearly Degenerate; Entropy Condition



In this paper, we solve the Riemann problem with the initial data containing Dirac delta functions for the Chaplygin pressure Aw-Rascle traffic model. With the characteristic analysis, under the suitably generalized Rankine-Hugoniot relation and entropy condition, we constructively obtain the global generalized solutions that explicitly exhibit four kinds of different structures involving delta shock waves.

李建业. 带有Chaplygin压强的Aw-Rascle交通模型含有狄拉克函数初值的黎曼问题[J]. 应用数学进展, 2013, 2(3): 114-126. http://dx.doi.org/10.12677/AAM.2013.23015


[1] M. Godvik, H. Hanche-Olsen. Existence of solutions for the Aw-Rascle traffic flow model with vacuum. Journal of Hyperbolic Differential Equations, 2008, 5(1): 45-63.
[2] M. Sun. Interactions of elementary waves for the Aw-Rascle model. SIAM Journal on Applied Mathematics, 2009, 69(6): 1542-1558.
[3] C. Shen, M. Sun. Formation of delta shocks and vacuum states in the vanishing pressure limit of Riemann solutions to the perturbed Aw-Rascle model. Journal of Differential Equations, 2010, 249(12): 3024-3051.
[4] L. Pan, X. Han. The Aw-Rascle traffic model with Chaply-gin pressure. Journal of Mathematical Analysis and Applications, 2013, 401(1): 379- 387.
[5] P. Goatin. The Aw-Rascle vehicular traffic flow model with phase transitions. Mathematical and Computer Modelling, 2006, 44(3): 287-303.
[6] Y. Brenier. Solutions with concentration to the Riemann problem for the one-dimensional Chaplygin gas equations. Journal of Mathematical Fluid Mechanics, 2005, 7(3): 326-331.
[7] Z. K. Guo, Y. Z. Zhang. Cosmology with a variable Chaplygin gas. Physics Letters B, 2007, 645(4): 326-329.
[8] D. Serre. Multidimensional shock interaction for a Chaplygin gas. Archive for Rational Mechanics and Analysis, 2009, 191(3): 539-577.
[9] G. Lai, W. C. Sheng and Y. X. Zheng. Simple waves and pressure delta waves for a Chaplygin gas in two-dimensions. Discrete and Continuous Dynamical Systems, 2011, 31(2): 489-523.
[10] S. Chen, A. Qu. Two-dimensional Riemann problems for Chaplygin gas. SIAM Journal on Mathematical Analysis, 2012, 44(3): 2146-2178.
[11] H. C. Yang, W. H. Sun. The Riemann problem with delta initial data for a class of coupled hyperbolic systems of conservation laws. Nonlinear Analysis, 2007, 67(11): 3041-3049.
[12] Z. Wang, Q. L. Zhang. The Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Acta Mathematica Sci- entia, 2012, 32B(3): 825-841.
[13] H. Cheng, H. Yang. Riemann problem for the relativistic Chaplygin Euler equations. Journal of Mathematical Analysis and Applications, 2011, 381(1): 17-26.