Moving boundary problems and non-uniqueness for the thin film equation

A variety of mass preserving moving boundary problems for the thin film equation, ut = −(unuxxx)x, are derived (by formal asymptotics) from a number of regularisations, the case in which the substrate is covered by a very thin pre-wetting film being discussed in most detail. Some of the properties of the solutions selected in this fashion are described, and the full range of possible mass preserving non-negative solutions is outlined.