On the stability of the improved Aw–Rascle–Zhang model with Chaplygin pressure

The wave interactions of an improved Aw-Rascle-Zhang model with a non-genuinely nonlinear field

“…Sun [34] investigated interactions of elementary waves and found a new kind of wave named SJ, in which the shock wave S coincides with the contact discontinuity J. Liu and Sun [29] studied the wave interactions and stability of Riemann solutions for generalized Chaplygin gas. Chen, Jiang and Li [5] proved the stability of the IARZ model with Chaplygin pressure. However, there are few results about the wave interactions in traffic flow models with a non-genuinely nonlinear field [4,23,24].…”

“…According to Lemma 3.1 in [16], if F (u) satisfies the third inequality of (5), there is only one inflection point on the curves of the first family waves in the (ρ, q) plane. Thus the first characteristic family is non-genuinely nonlinear.…”

“…Thus the first characteristic family is non-genuinely nonlinear. Indeed, there exist F (u) satisfying (5).…”

“…The purpose of this paper is to show the wave interactions for the IARZ model (1) (4) (5) with three piecewise constant initial data (2), under the condition of nonconcave flow-density diagram in the first family wave curve. The phenomenon of merging traffic from other lanes to the current lane, which was represented as wave interactions [9] in the mathematical investigations of traffic flow models, occurs in reality frequently.…”

“…Then we decompose the problem into 16 cases of single elementary wave interactions and discuss the wave structures case by case. Finally, using the 16 cases as building blocks, we obtain the wave structures of solutions for the IARZ model (1) (4) (5) with three piecewise constant initial data (2).…”