  In this paper we show that thin shells in spherically symmetric spacetimes,
whose matter content is described by a pair of non-interacting spherically
symmetric matter fields, generically exhibit instability against an
infinitesimal separation of its constituent fields. We give explicit examples
and construct solutions that represent a shell that splits into two shells.
Then we extend those results for 5-dimensional Schwarzschild-AdS bulk
spacetimes, which is a typical scenario for brane-world models, and show that
the same kind of stability analysis and splitting solution can be constructed.
We find that a widely proposed family of brane-world models are extremely
unstable in this sense. Finally, we discuss possible interpretations of these
features and their relation to the initial value problem for concentrated
sources.
