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数苑博雅讲座

数苑讲座之十二:On H-system: an open question of Brezis-Coron and singularity formation

发布时间:2023-11-20 作者:77779193永利集团 浏览次数:
Speaker Juncheng Wei院士 DateTime 2023年11月23日(周四)下午4:30
Place 6号楼6401 Abstract In this talk I will discuss recent advances on $H-$system (surfaces with constant mean curvature)

$ \Delta u= H u_x \wedge u_y $

in a two-dimensional domain. First we show that all the $H-$bubbles are non-degenerate and then we consider a problem of singular perturbation
in the H-system with Dirichlet boundary condition on disk. As the boundary datum vanishes, we construct higher-degree multi-bubble
solutions concentrating at distinct points. This gives a partial answer to a conjecture due to Brezis-Coron  and Chanillo-Malchiodi concerning the limiting configuration in the case of higher degrees. Next  we
construct finite time blow-up for the heat flow of the H-system, describing the evolution of surfaces with constant mean curvature. The singularity at finite time forms as a scaled least energy H-bubble, denoted as W, exhibiting type II blow-up speed. One key observation is that the linearized operators around W projected onto $W^\perp$ and in the W-direction are in fact decoup...

魏军城,著名华人数学家,现任现为加拿大英属哥伦比亚大学国家讲座教授(Canada Research Chair),加拿大皇家科学院院士,主要研究领域是非线性偏微分方程、凝聚现象和爆破以及生物数学等,于2005年获得香港裘槎基金会(Croucher Foundation)“优秀科研者奖”,曾主持国家杰出青年基金,2010年获得华人数学家大会银奖,2010年获得教育部自然科学一等奖,2020年获加拿大数学会的Jefferey-Williams Prize,2014年应邀在第27届国际数学家大会上做45分钟报告,2014年入选国家级领军人才项目。