Instabilities in generic second-order traffic models with relaxation (Q6612979)

This paper deals with the second-order traffic model with relaxation \N\[\N \rho_t + (\rho v)_x=0,\qquad (\rho w)_t + (\rho wv)_x = \rho\frac{V(\rho )-v}{\tau}, \N\]\Nthe authors prove the existence of weak solutions, without requiring the sub-characteristic stability condition to hold. Using numerical simulations, they show how, in this unstable setting, large but bounded oscillations may arise from small perturbations of equilibria, thus reproducing the formation of stop-and-go waves commonly observed in traffic dynamics. Finally, they analyze the corresponding traveling waves.