題目一：Hydrodynamic model of semiconductors with sonic boundary: structure stability and quasi-neutral limit
内容簡介：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).
報告人：梅茗
報告人簡介：加拿大McGill大學兼職教授，Champlain學院終身教授，博士生導師，意大利L’Aquila大學客座教授，日本金澤大學合作教授。2015年被聘為吉林省長白山學者講座教授，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的研究，在ARMA,SIAM, JDE, Commun. PDEs 等刊物發表論文100多篇。其中有關帶時滞的反應擴散方程行波解穩定性的多篇系列性研究論文一直是ESI的高被引論文。梅茗教授是4家SCI國際數學雜志的編委，也是SlAM J Math Anal 和J Diff Equa 等重要刊物的 top author, 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。
題目二：Threshold convergence results for a nonlocal time-delayed diffusion equation
内容簡介：This talk is about the asymptotic behavior for nonlocal dispersion Nicholson blowflies equation. We obtain the threshold results with optimal convergence rates for the original solution to the constant equilibrium. This is a joint work with Prof. M. Mei and Dr. Z. Wang.
報告人：黃銳
報告人簡介：華南師範大學數學科學學院教授，博導。“廣東特支計劃”科技創新青年拔尖人才，重慶市“巴渝學者”講座教授，(國家)粵港澳應用數學中心副秘書長。主要從事非線性擴散方程的研究工作，先後主持國家自然科學基金、教育部及廣東省和廣州市各類科研項目多項，發表論文50餘篇。曾應邀赴法國馬賽大學，加拿大麥吉爾大學和香港理工大學等高校學術訪問。
時 間：2023年6月26日（周一）下午 15：00 始
地 點：南海樓124室
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2023年6月25日
