  We revisit a well-established model for highly re-entrant semi-conductor
manufacturing systems, and analyze it in the setting of states, in- and
outfluxes being Borel measures. This is motivated by the lack of optimal
solutions in the L1-setting for transitions from a smaller to a larger
equilibrium with zero backlog. Key innovations involve dealing with
discontinuous velocities in the presence of point masses, and a finite domain
with in- and outfluxes. Taking a Lagrangian point of view, we establish
existence and uniqueness of solutions, and formulate a notion of weak solution.
We prove continuity of the flow with respect to time (and almost also with
respect to the initial state). Due to generally discontinuous velocities, these
delicate regularity results hold only with respect to carefully crafted
semi-norms that are modifications of the flat norm. Generally. the solution is
not continuous with respect to any norm on the space of measures.
