We prove the convergence of the vanishing viscosity approximation for a class of $ 2\times2 $ 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 $ L^1 $ 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.

中文翻译：

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\begin{document}$ 2\times 2 $\end{document} 系统建模拥堵车辆交通的消失粘度

我们证明了一类 $2\times2 $ 守恒定律系统的粘度消失近似的收敛性，其中包括拥挤状况下的交通流模型。系统的结构使我们能够避免对初始数据的总变异和 $ L^1 $ 范数的典型约束。关键工具是由 Murat 和 Tartar 引入的补偿紧凑性技术，这里在 Panov 开发的框架中使用。黎曼不变量的结构用于获得紧凑性估计。