报告题目：Structural stability of subsonic steady-states to hydrodynamic model for semiconductors with sonic boundary

报 告 人：梅茗教授 McGill University & Champlain College

报告时间：2022年08月03日 08:30-09:30

报告地点：腾讯会议 ID：728-3870-4890

或点击链接直接加入会议：https://meeting.tencent.com/dm/OIQ1fh7H3ONY

校内联系人：刘长春 liucc@jlu.edu.cn

报告摘要：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.

报告人简介：梅茗教授，加拿大McGill大学兼职教授及Champlain学院的终身教授，博士生导师。2015年被聘为吉林省“长白山学者”讲座教授，以及东北师范大学“东师学者”讲座教授。主要从事流体力学中偏微分方程和生物数学中带时滞反应扩散方程研究，在ARMA, SIAM, JDE, Commun.PDEs 等高水平杂志上发表论文100多篇，是多家SCI国际数学杂志的编委。并一直承担加拿大自然科学基金项目，魁北克省自然科学基金项目，及魁北克省大专院校国际局的基金项目。