  Recently, results regarding the Inverse Design problem for Conservation Laws
and Hamilton-Jacobi equations with space-dependent convex fluxes were obtaine.
More precisely, characterizations of attainable sets and the set of initialdata
evolving at a prescribed time into a prescribed profile were obtained. Here,
wepresent an explicit example that underlines deep diff erences between the
space-dependentand space-independent cases. Moreover, we add a detailed
analysis of the time asymptoticsolution of this example, again underlining diff
erences with the space-independent case.
