報告題目：Structural stability of subsonic steady-states to hydrodynamic model for semiconductors with sonic boundary
報 告 人：梅茗教授 McGill University & Champlain College
報告時間：2022年08月03日 08:30-09:30
報告地點：騰訊會議 ID：728-3870-4890
或點擊鍊接直接加入會議：https://meeting.tencent.com/dm/OIQ1fh7H3ONY
校内聯系人：劉長春 liucc@jlu.edu.cn
報告摘要：For the hydrodynamic model for semiconductors with sonic boundary, represented by Euler-Poisson equations, it possesses the various physical steady-states including interior-subsonic/interior-supersonic/shock-transonic/$C^1$-smooth-transonic steady-states. Since these physical steady-states reduce some serious singularities at the sonic boundary (their gradients are infinity), this makes that the structural stability for these physical solutions is more difficult and challenging, and has remained open as we know. In this talk, I will present a recent study on the structural stability of interior subsonic steady-states. Namely, when the doping profiles are as small perturbations, the differences between the corresponding subsonic solutions are also small. To overcome the singularities at the sonic boundary, we propose a new technique combining by the weighted energy estimates, the local singularity analysis, and the monotonicity argument. Both the result itself and techniques developed here will give us some truly enlightening insights into our follow-up study on the structural stability of the remaining types of solutions.
報告人簡介：梅茗教授，加拿大McGill大學兼職教授及Champlain學院的終身教授，博士生導師。2015年被聘為吉林省“長白山學者”講座教授，以及東北師範大學“東師學者”講座教授。主要從事流體力學中偏微分方程和生物數學中帶時滞反應擴散方程研究，在ARMA, SIAM, JDE, Commun.PDEs 等高水平雜志上發表論文100多篇，是多家SCI國際數學雜志的編委。并一直承擔加拿大自然科學基金項目，魁北克省自然科學基金項目，及魁北克省大專院校國際局的基金項目。
