【学术预告】数学与统计学院学术预告二则

报告题目一：Moment propagation of the plasma-charge model with a time-varying magnetic field

报告人：张显文

报告时间：12月01日（周五）16:00-18:00

报告地点：数学楼315会议室

报告摘要：In this paper, we prove the global existence and moment propagation of weak solutions for the repulsive plasma-charge model with a time-varying magnetic field. Multi-point charges are allowed according to an improved mechanism to compensate the asymmetry caused by the point charges, which brings us back to the standard Lions- Perthame's argument. To deal with two type singularities induced by the point charges and the magnetic field, we combine the ideas from Desvillettes-Miot-Saffirio(Ann. Inst. H. PoincaréAnal. Non Linéaire, 2015) and Rege(SIAM J. Math. Anal. 2021). The macroscopic density of the plasma is allowed to be constant around the point charges, by applying the moment lemma established by Perthame and careful compactness argument. The result answers two questions raised by Desvillettes-Miot-Saffirio(Ann. Inst. H. Poincaré Anal. Non Linéaire, 2015).

报告人简介：张显文，博士，华中科技大学数学与统计学院教授、博士生导师, 研究领域为非线性偏微分方程，目前主要关注Vlasov-Poisson系统、非线性Boltzmann方程以及其他各种动理学方程的整体适定性、正则性传播以及大时间行为等问题。主持和参加多项国家自然科学基金项目，在Commum.Math.Phys., SIAM J.Math.Anal., J.Differential Equations等国内外学术期刊上发表论文80余篇。

报告题目二：Recent progress of the perfect and insulated conductivity problems

报告人：董弘桀

报告时间：12月06日（周三）09:30-11:30

报告地点：腾讯会议（388-619-397）

报告摘要：In the first part of the talk, I will present our work about the insulated conductivity problem with closely spaced inclusions in a bounded domain in $R^n$. A noteworthy phenomenon in this context is the potential for the gradient of solutions to blow up as the distance between inclusions tends to zero.We obtained an optimal gradient estimate of solutions in terms of the distance, which settled down a major open problem in this area. In the second part, I will discuss recent results about the insulated and perfect conductivity problems when the current-electric field relation is a power law. Based on joint work with Yanyan Li (Rutgers University), Zhuolun Yang and Hanye Zhu (Brown University).

报告人简介：Hongjie Dong is a Professor at the Division of Applied Mathematics of Brown University. He received his Ph.D. in 2005 at the Department of Mathematics in the University of Minnesota. Prof. Dong's current research interests include Partial Differential Equations, Probability, and Numerical Analysis. He was the recipient of an NSF early career award in 2011 and a Simons fellowship in 2021. He has also been on the editorial boards of several journals including SIAM J. Math. Anal. and J. Differential Equations.