本周五院学术报告-10月23日


(1) 题目: Existence and local uniqueness of bubbling solutions for poly-harmonic equations

报告人: 彭双阶教授 (华中师范大学数学与统计学院院长)

时间与地点: 2015年10月23日, pm4:00-5:00, 后主楼1124

邀请人: 保继光 教授

摘要:We will construct infinitely many solutions with infinitely bubbling for a poly-harmonic equation with critical growth. We also give a local uniqueness result for the bubbling solutions, which implies that some bubbling solutions can preserve  the symmetry of the equation.

(2)题目: Soliton resolution for nonlinear wave equation 

报告人:北京大学 刘宝平博士。刘博士本科毕业于北京大学,在加州大学伯克利分校获得博士学位,师从国际著名偏微分方程专家Daniel Tataru,2012--2015 为芝加哥大学数学系博士后,合作导师美国科学院院士Carlos Kenig  Wilhelm Schlag

时间和地点: 2015年10月23日, pm3:00-4:00, 后主楼1124

邀请人: 熊金钢

Abstract: In this talk, we consider nonlinear dispersive Hamiltonian equations with large initial data. Our focus is the long term dynamics of their solutions.

In the mathematical physics community, there has been a widespread belief that, large global solutions of dispersive equations should eventually resolve into a superposition of a free radiation component plus a finite number of nonlinear bound states.  This is called the ‘soliton resolution conjecture’, which remains wide open except for few cases of integrable equations with sufficiently nice initial data.

I will present some recent results where we manage to verify the conjecture for specific models. I will explain some of the main ingredients in our proof, and elaborate the ‘channel of energy’ inequality discovered by T. Duyckaerts, C. Kenig and F. Merle.

 

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