演講公告

演講主題：Some results on the finite point blow-up solutions of the fast diffusion equation
主講人：許健明教授(中央研究院數學研究所)
演講日期：2018年2月27日(星期二) 14:00 –15:00
演講地點：(光復校區) 科學一館223室
茶會時間：2018年2月27日13:30 (科學一館205室)
摘要內容：
Abstract. In this talk I will prove the existence and asymptotic large time behaviour of singular solutions of the fast diffusion equation $u_t=\Delta u^m$, $u>0$, in $(\mathbb{R}^n\setminus\{0\})\times (0,\infty)$ for any $0<m<\frac{n-2}{n}$, $n\ge 3$. We will construct self-similar solutions of the fast diffusion equation in $(\mathbb{R}^n\setminus\{0\})\times (0,\infty)$ with initial value $A|x|^{-\gamma}$ for some constant $\frac{2}{1-m}<\gamma<\frac{n-2}{m}$. When $\frac{2}{1-m}<\gamma<n$, we prove that if the initial data is some weighted $L^1$ perturbation of such self-similar singular solution, the singular solution of the fast diffusion equation will converge to the self-similar singular solution as time goes to infinity. This is joint work with Soojung Kim.
相關檔案：Talk_1070227.pdf

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