  Consider a Conservation Law and a Hamilton-Jacobi equation with a
ux/Hamiltonian depending also on the space variable. We characterize rst the
attainable set of the two equations and, second, the set of initial data
evolving at a prescribed time into a prescribed prole. An explicit example then
shows the deep dierences between the cases of x-independent and x-dependent
uxes/Hamiltonians.
