Speaker: Galina Perelman （LAMA, Université Paris- Est Créteil)
Time: 15:00-17:00 August 19 & August 21
Room: 1418,management and research building
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.
