报告人：梅 茗 教授
主持人：张晓颖 院长
时 间：2023年7月14日 星期五 上午10:00 - 11:00
地 点：综合楼A区402
主办单位：bet356体育理学院
报告人简介：梅茗，加拿大McGill大学及Champlain College教授, 博士生导师。意大利L’Aquila大学客座教授，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。
观点综述：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).
