【online】Summer 2020 online talks on partial differential equations
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Summer 2020 online talks on partial differential equations
题目: Regularity, extinction and bubbling for fast diffusion equations in bounded domains
报告人：金天灵 (The Hong Kong University of Science and Technology)
时间： 2020年8月11日 10:00-11:00
报告方式：Zoom会议室 ID: 681 7076 5815 密码: 20200804
摘要: We will first show optimal boundary regularity for bounded positive weak solutions of fast diffusion equations in smooth bounded domains. This solves a problem raised by Berryman and Holland in 1980 for these equations in the subcritical and critical regimes. Then we study extinction profiles of solutions to Sobolev critical fast diffusion equations with the Brezis-Nirenberg effect. We show that the convergence rates of the relative error in regular norms are at least polynomial. Exponential decay rates are proved for generic domains. Results for Sobolev subcritical fast diffusion equations are also obtained. Our proof makes use of regularity estimates, a curvature type evolution equation, as well as blow up analysis. This is joint work with Jingang Xiong.
The upcoming talks will be updated on http://maths.nju.edu.cn/~xzchen/Summer2020.pdf .
邀请人：陈学长 老师、李军 老师