论文标题
非本地流量模型的极限解决方案的熵可接受性
Entropy Admissibility of the Limit Solution for a Nonlocal Model of Traffic Flow
论文作者
论文摘要
我们考虑了交通流的保护法模型，其中每辆车的速度取决于交通密度的加权平均值$ρ$。平均内核是指数类型：$ w_ \ varepsilon（s）= \ varepsilon^{ - 1} e^{ - s/\ s/\ varepsilon} $。对于任何降低速度函数$ v $，我们证明，作为$ \ varepsilon \至0 $，非处方方程的解决方案的极限与标量保护法的唯一熵 - 可加入的解决方案相吻合$ρ_T +（ρvv（ρv（ρ））_ x = 0 $。
We consider a conservation law model of traffic flow, where the velocity of each car depends on a weighted average of the traffic density $ρ$ 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 $ρ_t + (ρv(ρ))_x=0$.
