中科院数学与系统科学研究院
数学研究所
调和分析及其应用研究中心
学术报告
调和分析和偏微分方程研讨班
报告人：熊金钢 （北师大）
题 目：Bubbling and extinction for some fast diffusion equations in bounded domains
时 间：2023.10.31（星期二）10:00-11:00
地 点：思源楼S813
摘 要：Motivated by the Wisconsin octupole experiments on anomalous diffusion of hydrogen plasma across a purely poloidal octupole magnetic field, Berryman-Holland 1980 proved the stability of separable solutions of the Sobolev subcritical fast diffusion equation in bounded domains with the homogeneous Dirichlet boundary condition. Berryman-Holland’s stability was along a subsequence in the $H_0^1$ topology. A satisfactory answer to the stability has been provided recently, which I will report first. Subsequently, I will talk about the Sobolev critical regime. I will show bubbling, soliton resolution in $C^0$ space as well as convergence with the aid of Brezis-Nirenberg effect. This is joint with Tianling Jin.
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