  Fundamental global similarity solutions of the standard form
u_\g(x,t)=t^{-\a_\g} f_\g(y), with the rescaled variable y= x/{t^{\b_\g}},
\b_\g= \frac {1-n \a_\g}{10}, where \a_\g>0 are real nonlinear eigenvalues (\g
is a multiindex in R^N) of the tenth-order thin film equation (TFE-10) u_{t} =
\nabla \cdot(|u|^{n} \n \D^4 u) in R^N \times R_+, n>0, are studied. The
present paper continues the study began by the authors in the previous paper
  P. Alvarez-Caudevilla, J.D.Evans, and V.A. Galaktionov, The Cauchy problem
for a tenth-order thin film equation I. Bifurcation of self-similar oscillatory
fundamental solutions, Mediterranean Journal of Mathematics, No. 4, Vol. 10
(2013), 1759-1790.
  Thus, the following questions are also under scrutiny:
  (I) Further study of the limit n \to 0, where the behaviour of finite
interfaces and solutions as y \to infinity are described. In particular, for
N=1, the interfaces are shown to diverge as follows: |x_0(t)| \sim 10 \left(
\frac{1}{n}\sec\left( \frac{4\pi}{9} \right) \right)^{\frac 9{10}} t^{\frac
1{10}} \to \infty as n \to 0^+.
  (II) For a fixed n \in (0, \frac 98), oscillatory structures of solutions
near interfaces.
  (III) Again, for a fixed n \in (0, \frac 98), global structures of some
nonlinear eigenfunctions \{f_\g\}_{|\g| \ge 0} by a combination of numerical
and analytical methods.
