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.
海报
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