题 目：On the dynamics of semilinear wave equations with energy supercritical growth

报告人：杨建伟 北京理工大学

报告时间：2023年12月17日  18:30-21:30

腾讯会议号：794 364 7383

摘要：We study the longtime dynamics of the solutions of semilinear wave equations with an energy supercritical growth. The theory of nonlinear wave equations has attacted intense study in the latest three decades, especially on its longtime dynamical behavior generated by the nonlinear effects, such as the scattering theory, blow-up and the stability/instability of solutions etc. The equation in question is a typical model of infinite dimensional dynamical system so that plenty of wave phenomena arising from strong physical background are predictable by studying this model. The ongoing research in the academic community focus on the energy critical case, culminating the celebrated soliton resolution theory of Duyckaerts Kenig Merle (DKM). Concerning the energy supercritical case, very few results are known and many things to be explored. In this talk, we shall go through the study on the energy supercritical wave equations and some remarkable results as well as some open questions. We shallalso investigate its natural variant on the exterior domain, openning up a complerely new landscape compared with the whole space. In particular, we shall give a rather precise description on the dynamics in a neighborhood of stationary solutions. We clarify the use of DKM's channel of energy method, and present some recent results on the global centerstable manifold theory, highlighting the one-pass theorem, as well as the instability of blowup solutions. This work is joint with professor Thomas Duyckaerts (LAGA, Paris Nord).

报告人简介: 杨建伟，北京理工大学数学科学学院特别研究员，研究方向为调和分析与偏微分方程。2015年博士毕业于中国工程物理研究院。后在北京大学数学中心从事博士后研究，导师为田刚院士。2016-2017 年于法国巴黎北部大学伽利略研究所从事博士后研究，导师为Thomas Duyckaerts 教授，2019 年获得cergy-pontoise大学Labex项目，于LAGA 从事学术访问工作。2018年入职北京理工大学。杨建伟与合作者在Kakeya问题，拉普拉斯的特征函数估计问题等调和分析热点问题中已做出多项重要成果，在非线性波动方程的动力学行为等国际前沿课题做出重要工作，相关成果发表在Analysis &PDE，Annales de l’institut Fourier, Journal of Functional Analysis, Sci. Math.China, Studia Math., Communications in Contemporary Mathematics Forum Mathematicum等国内外学术期刊上。