On the stability of the improved Aw-Rascle-Zhang model with Chaplygin pressure (Q2665483)

This paper deals with the improved Aw-Rascle-Zhang model \[ \rho_t + (\rho u)_x = 0,\qquad (\rho(F (u) + p(\rho)))_t + (\rho u(F (u) + p(\rho)))_x = 0, \] with Chaplygin pressure \[ p(\rho) = -\frac{1}{\rho}. \] On the function \(F\) the authors assume \[ F'(u) > 0,\qquad F''(u)> 0. \] They solve the Riemann problem and analyze the wave interactions in detail to get the stability of the solutions.