报告人：熊金钢
报告地点：腾讯会议ID:460349764; 会议密码:110923
报告时间：2023年11月09日星期四15:00-16:00
邀请人：李勇、冀书关
报告摘要：
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.
主讲人简介：
熊金钢，北京师范大学教授、博导，国家杰出青年科学基金和国家优秀青年科学基金获得者。主要从事变分法、椭圆与抛物型偏微分方程研究，解决Berryman和Holland 1980年提出的快速扩散方程正则性猜想，被菲尔茨奖得主论文评价称“ingenious” & “remarkable”；解决Monge-Ampère方程、Yamabe方程以及奇异调和映照中的若干长期未解的奇点结构问题；开启非局部Nirenberg问题等临界非线性问题的研究。迄今在国际期刊《Amer. J. Math.》, 《J. Eur. Math. Soc.》, 《J. Reine Angew. Math.》，《Proc. London Math. Soc.》等发表论文近 40 篇。
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