报告题目：A stylized pyramid-shaped blow-up set for the 2d semilinear wave equation
报告人：Hatem Zaag（法国巴黎第十三大学教授）
报告时间：2020年12月3日14时00分
腾讯会议号：313 102 049
邀请人：程星
报告摘要：
We consider the semilinear wave equation with subconformal power nonlinearity in two space dimensions. We construct a finite-time blow-up solution with an isolated characteristic blow-up point at the origin, and a blow-up surface which is centered at the origin and has the shape of a stylized pyramid, whose edges follow the bisectrices of the axes in R2. The blow-up surface is differentiable outside the bisectrices. As for the asymptotic behavior in similarity variables, the solution converges to the classical one-dimensional soliton outside the bisectrices. On the bisectrices outside the origin, it converges (up to a subsequence) to a genuinely two-dimensional stationary solution, whose existence is a by-product of the proof. At the origin, it behaves like the sum of 4 solitons localized on the two axes, with opposite signs for neighbors.
This is the first example of a blow-up solution with a characteristic point in higher dimensions, showing a really two-dimensional behavior. Moreover, the points of the bisectrices outside the origin give us the first example of non-characteristic points where the blow-up surface is non-differentiable. This is a joint work with Frank Merle, Cergy Paris University and IHES.
报告人简介：
Hatem Zaag，法国巴黎第十三大学教授，分析、几何及其应用实验室主任。主要从事偏微分方程的研究。曾主持欧洲和法国的多项科学基金。Hatem Zaag教授共发表70多篇学术论文，特别地，在Comm. Pure Appl. Math., Duke Math.J.,Math. Ann., J. Math. Pures Appl., Comm. Math. Phys., Amer.J. Math., Comm. Partial Differential Equations等国际著名数学杂志发表重要研究工作，他的工作受到国内外同行的广泛关注。