Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (6): 1353-1371.

• Articles • Previous Articles     Next Articles

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

 SHAO Zhi-Qiang   

  1. 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.

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

CLC Number: 

  • 35L65
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