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

Abstract

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 $t\to \infty$.

arXiv comment21 pages. arXiv admin note: text overlap with arXiv:1712.05515