Abstract: A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries (KdV) equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.

Key words: linear periodic system; parameter uncertainty;robust stability;linear matrix inequality (LMI);state feedback;stabilization;$\mathcal{L}_2$-gain, conservative scheme, hyperbolic conservation law, higher-order traffic flow model, traveling wave solution