We consider a conservation law model of traffic flow, where the velocity of each car depends on a weighted average of the traffic density $\rho$ ahead. The averaging kernel is of exponential type: $w_\varepsilon (s)=\varepsilon^{-1} e^{-s / \varepsilon}$. For any decreasing velocity function $v$, we prove that, as $\varepsilon \to 0$, the limit of solutions to the nonlocal equation coincides with the unique entropy-admissible solution to the scalar conservation law $\rho_t + {(\rho v(\rho))}_x = 0$.

中文翻译：

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非局部交通流模型极限解的熵可容许性

我们考虑交通流的守恒定律模型，其中每辆车的速度取决于前方交通密度 $\rho$ 的加权平均值。平均核是指数型的：$w_\varepsilon (s)=\varepsilon^{-1} e^{-s / \varepsilon}$。对于任何速度递减函数 $v$，我们证明，当 $\varepsilon \to 0$ 时，非局部方程的解的极限与标量守恒定律 $\rho_t + {(\ rho v(\rho))}_x = 0$。