報告人：梅 茗 教授

主持人：張曉穎 院長

時 間：2023年7月14日 星期五 上午10:00 - 11:00

地 點：綜合樓A區402

主辦單位：長春大學理學院

報告人簡介：梅茗，加拿大McGill大學及Champlain College教授, 博士生導師。意大利L’Aquila大學客座教授，吉林省“長白山學者”講座教授，以及東北師范大學“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滯反應擴散方程研究，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。

觀點綜述：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 estimates. For the quasi-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. This talk is based on two recent research papers published in SIAM J. Math. Anal. (2023).