報告題目：Hydrodynamic model of semiconductors with sonic boundary: structure stability and quasi-neutral limit
報告人：梅茗教授 McGill University & Champlain College 加拿大
報告時間：2023年8月15日 9:30-10:30
報告地點：騰訊會議 ID：775-702-622
校内聯系人：劉長春 liucc@jlu.edu.cn
報告摘要：This talk is concerned with the structural stability of subsonic steady states and quasi-neutral limit to one-dimensional steady hydrodynamic model of semiconductors in the form of Euler-Poisson equations with degenerate boundary, a difficult case caused by the boundary layers and degeneracy. We first prove that the subsonic steady states are structurally stable, once the perturbation of doping profile is small enough. To overcome the singularity at the sonic boundary, we introduce an optimal weight in the energy edtimates. For the quadi-neutral limit, we establish a so-called convexity structure of the sequence of subsonic-sonic solutions near the boundary domains in this limit process, which efficiently overcomes the degenerate effect.On this account, we first show the strong convergence in $L^2$ norm with the order $O(\lambda^\frac{1}{2})$ for the Debye length $\lambda$ when the doping profile is continuous. Then we derive the uniform error estimates in $L^\infty$ norm with the order $O(\lambda)$ when the doping profile has higher regularity.
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 J. Math. Anal., 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。
