  Consider the inverse design problem for a scalar conservation law, i.e., the
problem of finding initial data evolving into a given profile at a given time.
The solution we present below takes into account localizations both in the
final interval where the profile is assigned and in the initial interval where
the datum is sought, as well as additional a priori constraints on the datum's
range provided by the model. These results are motivated and can be applied to
data assimilation procedures in traffic modeling and accidents localization.
