主讲人简介：

梅茗，加拿大McGill大学兼职教授，Champlain学院终身教授，博士生导师，意大利L'Aquila大学客座教授，日本金泽大学合作教授。2015年被聘为吉林省长白山学者讲座教授，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的研究，在ARMA，SIAM, JDE, Commun. PDEs等刊物发表论文100多篇。其中有关带时滞的反应扩散方程行波解稳定性的多篇系列性研究论文一直是ESI的高被引论文。梅茗教授是4家SCI国际数学杂志的编委，也是SlAM J Math Anal 和J Diff Equa等重要刊物的top author, 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。

内容摘要：

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.  This talk is based on two recent research papers published in SIAM J. Math. Anal. (2023).

主持人：秦玉明

撰写：李学元