  We study the question of uniqueness of weak solution to the fast reaction
limit of the Keller and Rubinow model for Liesegang rings as introduced by
Hilhorst et al. (J. Stat. Phys. 135, 2009, pp. 107-132). The model is
characterized by a discontinuous reaction term which can be seen as an instance
of spatially distributed non-ideal relay hysteresis. In general, uniqueness of
solutions for such models is conditional on certain transversality conditions.
For the model studied here, we give an explicit description of the
precipitation boundary which gives rise to two scenarios for non-uniqueness,
which we term "spontaneous precipitation" and "entanglement". Spontaneous
precipitation can be easily dismissed by an additional, physically reasonable
criterion in the concept of weak solution. The second scenario is one where the
precipitation boundaries of two distinct solutions cannot be ordered in any
neighborhood of some point on their common precipitation boundary. We show that
for a finite, possibly short interval of time, solutions are unique. Beyond
this point, unique continuation is subject to a spatial or temporal
transversality condition. The temporal transversality condition takes the same
form that would be expected for a simple multicomponent semilinear ODE with
discontinuous reaction terms.
