报告题目：Blow-up, scattering and invariant manifolds: long-time dynamics of nonlinear wave equations of energy super-critical growth
报告人：杨建伟（北京理工大学特别副研究员）
报告时间：2020年6月30日15时15分-16时15分
腾讯会议号：853 651 696，密码：0630
邀请人：程 星
报告摘要：
We study the focusing nonlinear wave equation (NLW) outside a ball subject to the Dirichlet boundary condition with energy super-critical nonlinearity. This equation admits finite-time blow-up solutions and a countable sequence of radial stationary solutions. We classify all radial stationary solutions and prove that all radial global solutions of NLW are asymptotically the sum of a stationary solution and a radiation term. We shall also study the local dynamics around a stationary solution: construct center-stable manifolds close to every stationary solution and show that the solutions scattering to the stationary solution in question weave out a Lipschitz manifold of finite codimension, which is invariant under the flow of nonlinear wave. We conjecture the set O, of initial data leading to finite-time blow-up solutions is open, whose boundary coincides with the invariant manifolds, which separates O away from the open set of scattering solutions. This work is joint with Thomas Duyckaerts (LAGA (UMR 7539), Université Paris 13).
报告人简介：
杨建伟主要从事调和分析与偏微分方程的研究，曾在北京国际数学中心和巴黎十三大从事博士后研究工作。目前主持国家自然科学基金青年基金。杨建伟博士已发表11篇SCI学术论文， 特别地，在Anal. PDE, J. Funct. Anal., Commun. Contemp. Math.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。