  The 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. The paper also
provides results which indicate that nudging can increase the flow in a
ring-road and, if properly designed, can have a strong stabilizing effect on
traffic flow. More specifically, the paper gives results which guarantee local
exponential stability of the uniform equilibrium in the L2 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.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.
