导航
学术报告|
当前位置:首页  科研  学术报告
报告题目: Soliton resolution for the sine-Gordon equation
报 告 人: 陆冰滢 博士
报告人所在单位: University of Bremen
报告日期: 2021-08-18 星期三
报告时间: 14:30--15:30
报告地点: 腾讯会议 ID: 525 721 484
   
报告摘要:
In this talk, we study the long-time dynamics and stability properties of the sine-Gordon equation f_{tt}−f_{xx}+/sin f=0. Firstly, we use the nonlinear steepest descent for Riemann-Hilbert problems to compute the long-time asymptotics of the solutions to the sine-Gordon equation whose initial condition belongs to some weighted Sobolev spaces. Secondly, we study the asymptotic stability of the sine-Gordon equation. It is known that the obstruction to the asymptotic stability of the sine-Gordon equation in the energy space is the existence of small breathers which is also closely related to the emergence of wobbling kinks. Combining the long-time asymptotics and a refined approximation argument, we analyze the asymptotic stability properties of the sine-Gordon equation in weighted energy spaces. Our stability analysis gives a criterion for the weight which is sharp up to the endpoint so that the asymptotic stability holds.
   
本年度学院报告总序号: 214

Copyright © |2012 复旦大学数学科学学院版权所有 沪ICP备042465