  This paper is devoted to some aspects of well-posedness of the Cauchy problem
for a quasilinear degenerate fourth-order parabolic thin film equation u_{t} =
-\nabla \cdot(|u|^{n} \nabla\D u) in \ren \times \re_+, \quad u(x,0)=u_0(x) in
\ren, where $n>0$ is a fixed exponent, with bounded smooth compactly supported
initial data. Dealing with the CP (for, at least, $n \in (0, \frac 32)$)
requires introducing classes of infinitely changing sign solutions that are
oscillatory close to finite interfaces.
  The main goal of the paper is to detect proper solutions of the CP for the
degenerate TFE--4 by uniformly parabolic analytic $\e$-regularizations at least
for values of the parameter $n$ sufficiently close to 0.
