Consider a nonlocal conservation law where the flux function depends on the convolution of the solution with a given kernel. In the singular local limit obtained by letting the convolution kernel converge to the Dirac delta one formally recovers a conservation law. However, recent counter-examples show that in general the solutions of the nonlocal equations do not converge to a solution of the conservation law. In this work we focus on nonlocal conservation laws modeling vehicular traffic: in this case, the convolution kernel is anisotropic. We show that, under fairly general assumptions on the (anisotropic) convolution kernel, the nonlocal-to-local limit can be rigorously justified provided the initial datum satisfies a one-sided Lipschitz condition and is bounded away from 0. We also exhibit a counter-example showing that, if the initial datum attains the value 0, then there are severe obstructions to a convergence proof.

考虑一个非局部守恒定律，其中通量函数取决于解与给定内核的卷积。在通过让卷积核收敛到狄拉克 delta 获得的奇异局部极限中，一个形式上恢复了守恒定律。然而，最近的反例表明，一般来说，非局部方程的解不会收敛到守恒定律的解。在这项工作中，我们专注于对车辆交通建模的非局部守恒定律：在这种情况下，卷积核是各向异性的。我们表明，在（各向异性）卷积核的相当一般的假设下，如果初始数据满足单边 Lipschitz 条件并且远离 0，则可以严格证明非局部到局部的限制。我们还展示了一个计数器- 示例表明，