This paper provides conditions that guarantee existence and uniqueness of classical solutions for a non-local conservation law on a ring road with possible nudging (or ‘look behind’) terms. The obtained conditions are novel, as they are not covered by existing results in the literature. This paper also provides results which indicate that nudging can increase the flow in a ring road and, if properly designed, can have a strong stabilising effect on traffic flow. More specifically, this paper gives results that guarantee local exponential stability of the uniform equilibrium profile in the $L^2$ state norm even for cases where the uniform equilibrium profile in a ring road without nudging is not asymptotically stable and the model admits density waves. The efficiency of the use of nudging terms is demonstrated by means of a numerical example.

本文提供了条件，以保证环路上非局部守恒定律的经典解决方案的存在性和唯一性，其中可能包含轻推（或“向后看”）术语。获得的条件是新颖的，因为它们没有被文献中的现有结果所涵盖。本文还提供的结果表明，轻推可以增加环路中的流量，如果设计得当，可以对交通流量产生强大的稳定作用。更具体地说，本文给出的结果保证了均匀平衡分布的局部指数稳定性${\mathrm{大号}}^2$即使在没有轻推的环形道路上的均匀平衡轮廓不是渐近稳定的并且模型允许密度波的情况下，状态规范也是如此。通过一个数值例子证明了使用轻推术语的效率。