Open AccessVanishing viscosity for a $ 2\times 2 $ system modeling congested vehicular traffic
Author(s) -
Giuseppe Maria Coclite,
Nicola De Nitti,
Mauro Garavello,
Francesca Marcellini
Publication year - 2021
Publication title -
networks and heterogeneous media
Language(s) - English
Resource type - Journals
eISSN - 1556-181X
pISSN - 1556-1801
DOI - 10.3934/nhm.2021011
Subject(s) - compact space , conservation law , viscosity , mathematics , norm (philosophy) , convergence (economics) , viscosity solution , pure mathematics , mathematical analysis , physics , thermodynamics , political science , law , economics , economic growth
We prove the convergence of the vanishing viscosity approximation for a class of \begin{document}$ 2\times2 $\end{document} systems of conservation laws, which includes a model of traffic flow in congested regimes. The structure of the system allows us to avoid the typical constraints on the total variation and the \begin{document}$ L^1 $\end{document} 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.