【Galina Perelman 】研究生教育创新计划高水平学术前沿讲座



Mini-Course IIBlow up dynamics for the hyperbolic vanishing mean curvature flow of surfaces asymptotic to Simons cone
主讲人Galina Perelman   (LAMA, Université Paris- Est Créteil)
时间8月19日      下午  15:00-17:00
           8月21日      下午  15:00-17:00
地点东区管理科研楼   澳门新葡新京1418室

摘要In these lectures I am going to address the question of finite time blow up for the hyperbolic vanishing mean curvature flow of surfaces in $/mathbb{R}^8$ asymptotic at infiniity to Simons cone: 
$$/mathcal{C}_4=/{(x_1,/cdots,x_8)/in /mathbb{R}^8: x_1^2+/cdots+x_4^2=x_5^2+/cdots+x_8^2/}$$ 
This amounts to investigating the singularity formation for some second order quasilinear wave equation. The problem of singularity formation in finite time starting from smooth initial data is one of fundamental issues in the study of nonlinear hyperbolic PDEs and has attracted a lot of attention. Many recent works in this direction concern semilinear energy-critical and energy-supercritical wave type equations, studying type II blow up solutions that emerge from a dynamical rescaling of stationary states. The goal of these lecture is to show that this mechanism of blow up exists as well in the quasilinear model we are considering. 


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