Interaction of elementary waves for the Aw-Rascle traffic flow model with variable Lane width (Q2230525)

This paper deals with the following model describing the traffic flow on a road with variable width \[ \begin{cases} (a\rho )_t + (a\rho u)_x = 0,\\ (a\rho (u + p))_t + (a\rho u(u + p))_x = \rho upa_x ,\\ a_t=0, \end{cases} \] where \(\rho, u\) represent the density and the velocity of the vehicular traffic, \(p(\rho)=\rho^\gamma\) is the pressure law (or hesitation function) in traffic flows, and \(a(x)\) represents the lane width which depends on the location. The authors study the interaction of elementary waves, especially stationary wave interacting with rarefaction wave, shock wave and contact discontinuity.