  This paper study the two--phase problem for the forward-backward parabolic
equation with diffusion function of cubic type. Existence and uniqueness for
these kind of problems were obtained in literature in the case in which the
phases are both stable. Here we consider the situation in which the unstable
phase is taken in account, obtaining not trivial solution of the problem. It is
interesting to note that such solutions are given by solving generalized Abel's
equations.
