Let n ⩾ 3 and 0 < m < (n − 2)/n. We extend the results of Vazquez and Winkler (2011, J. Evol. Equ. 11, no. 3, 725–742) and prove the uniqueness of finite points blow-up solutions of the fast diffusion equation ut = Δum in both bounded domains and ℝn × (0, ∞). We also construct initial data such that the corresponding solution of the fast diffusion equation in bounded domain oscillates between infinity and some positive constant as t → ∞.

中文翻译：

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快速扩散方程有限点爆破解的唯一性及时间振荡行为

让n⩾ 3 和 0 <米< (n− 2)/n. 我们扩展了 Vazquez 和 Winkler (2011,J.进化。等。11，没有。3, 725–742) 并证明快速扩散方程的有限点爆破解的唯一性你吨= Δ你米在有界域和ℝn× (0, ∞)。我们还构造了初始数据，使得有界域中快速扩散方程的相应解在无穷大和某个正常数之间振荡吨→ ∞。