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arXiv · 1805.11449

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

Kin Ming Hui
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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 $t\to\infty$.

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Kin Ming Hui. 2018-05-26. Uniqueness and time oscillating behaviour of finite points blow-up solutions of the fast diffusion equation. https://arxiv.org/abs/1805.11449

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