Vanishing viscosity for a $ 2\times 2 $ system modeling congested vehicular traffic

Abstract

<p style='text-indent:20px;'>We prove the convergence of the vanishing viscosity approximation for a class of <inline-formula><tex-math id="M2">\begin{document}$ 2\times2 $\end{document}</tex-math></inline-formula> systems of conservation laws, which includes a model of traffic flow in congested regimes. The structure of the system allows us to avoid the typical constraints on the total variation and the <inline-formula><tex-math id="M3">\begin{document}$ L^1 $\end{document}</tex-math></inline-formula> norm of the initial data. The key tool is the compensated compactness technique, introduced by Murat and Tartar, used here in the framework developed by Panov. The structure of the Riemann invariants is used to obtain the compactness estimates.</p>