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.
Highlights
IntroductionWe study the Aw-Rascle (AR) macroscopic model of traffic flow ρt + ( ρu )x =0,
In the present paper, we study the Aw-Rascle (AR) macroscopic model of traffic flow ρt +x =0, ( ρ (u + P)) t + ( ρu (u P)) x = 0, (1)where ρ ≥ 0 is the density, u ≥ 0 is the velocity, P is the velocity offset which is called as the “pressure” inspired from gas dynamics
We find that the elementary wave interactions have a much more simple structure for Temple class than general systems of conservation laws
Summary
We study the Aw-Rascle (AR) macroscopic model of traffic flow ρt + ( ρu )x =0,. In [8], Aw and Rascle studied the limit behavior and found that the pressure term is active. In [10] [11], they studied the elementary wave interactions and obtained the stability of the Riemann solutions under such a perturbation on the initial data.
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