TITLE:
Wave Interactions of the Aw-Rascle Model for Generalized Chaplygin Gas
AUTHORS:
Yujin Liu
KEYWORDS:
Wave Interaction, Aw-Rascle Model, Generalized Chaplygin Gas, Riemann Problem, Delta Shock, Hyperbolic Conservation Laws
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.2,
February
26,
2021
ABSTRACT: In this paper, we investigate the elementary wave interactions of the Aw-Rascle model for the generalized Chaplygin gas. We construct the unique solution by the characteristic analysis method and obtain the stability of the corresponding Riemann solutions under such small perturbations on the initial values. We find that the elementary wave interactions have a much more simple structure for Temple class than general systems of conservation laws. It is important to study the elementary waves interactions of the traffic flow system for the generalized Chaplygin gas not only because of their significance in practical applications in the traffic flow system, but also because of their basic role for the general mathematical theory.