  We study self-similar solutions of the thin-film equation, with mobility
exponent m in (0,4], that describe the lifting of an isolated touch-down point
given by an initial profile of the form |x|. This provides a mechanism for
non-uniqueness of the thin-film equation with m in (2,4), since solutions with
a persistent touch-down point also exist in this case. In order to prove
existence of the self-similar solutions, we need to study a four-dimensional
continuous dynamical system. The proof consists of a shooting argument based on
the identification of invariant regions and on suitable energy formulas.
