Uniqueness and time oscillating behaviour of finite points blow-up solutions of the fast diffusion equation

Let $nge 3$ 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 $mathbb{R}^ntimes (0,infty)$. 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 $ttoinfty$.