  Let $n\ge 3$ and $0<m<\frac{n-2}{n}$. We will extend the results of J.L.
Vazquez and M. Winkler and prove the uniqueness of finite points blow-up
solutions of the fast diffusion equation $u_t=\Delta u^m$ in both bounded
domains and $\mathbb{R}^n\times (0,\infty)$. We will also construct initial
data such that the corresponding solution of the fast diffusion equation in
bounded domain oscillate between infinity and some positive constant as
$t\to\infty$.
