Global solutions and zero relaxation limit for a traffic flow model (Q2727764)

The author deals with the system of conservation laws of the form \(\rho_t+(\rho v)x=0\), \(v_t+(v^2/2+g(\rho))_x= (v_e(\rho)-v)/\tau\). Such a system arises in nonequilibrium continuous model of traffic flow. Existence theorem is proved by means of Glimm scheme, provided that initial data are of bounded total variation and of small distance to the equilibrium state \(v_e(\rho)=-a\rho +b\) \((a,b>0)\). Total variation of the solution is shown to be bounded independently of the relaxation paramter \(\tau\) and thus the zero relaxation limit is obtained. The limit satisfies the equilibrium equation. Finally, the author presents a comparison between obtained results and data measured on a freeway. This comparison yields qualitative agreement between analytical results and the data.