报告题目1：Linear elliptic equations and isoperimetric inequality

报告人：马力，北京科技大学

报告时间：2023年12月29日（周五）8:30-9:30

报告地点：20-404

报告摘要：The aim of this series of lectures is to know the behavior of global solutions to some typical parabolic equations/systems such as the curvature flow and minimal surface flows. As we will see, the boundary values of the problems play important roles in the study of the profiles of solutions. We also represent some result about stationary navier-Stokes equation.

In this first lecture, we consider some basic results such as the Sturm-Liouville theory, properties of harmonic functions, etc. We study the gradient estimate and prove Liouville theorem for harmonic functions. Then we introduce the maximum principles for linear elliptic equations of second order. We then solve the Poisson equation. We give applications of MP method to the proof of isoperimetric inequality in the Euclidean space.

报告题目2：Heat equations and Geometric flows

报告人：马力，北京科技大学

报告时间：2023年12月29日（周五）9:45-10:45

报告地点：20-404

报告摘要：In this talk, we first study the Leray’s question and recall some properties of the Sturm-Liouville operator. Then we obtain the solution to the 1-d heat equation.  For the higher dimensions, we present the maximum principle for the parabolic equation. We then study the global properties of heat equations. In the last part, we introduce the one dimensional geometric flows and study the behavior of the global solution.

报告题目3：1-d quasilinear parabolic flow

报告人：马力，北京科技大学

报告时间：2023年12月30日（周六）8:30-9:30

报告地点：20-404

报告摘要：In this talk, we study one dimensional geometric flows and study the behavior of the global solution. We give the detailed proof of the result obtained by Altschuler-Wu (1993, MA).

报告题目4：2-d minimal surface flow with the oblique derivative condition and translators

报告人：马力，北京科技大学

报告时间：2023年12月30日（周六）9:45-10:45

报告地点：20-404

报告摘要：In this lecture, we consider the existence problem of the minimal surface flow. We show Lebesgue space stability property of the straight lines along the one dimensional minimal surface flow. We study the global flow of two dimensional minimal surface flow. After introducing the translating solution, we study the asymptotic behavior of the global flow. Some questions are posed for the minimal surface system flows and related problems.

报告人简介：马力，北京科技大学教授，博士生导师。1989年博士毕业于中国科学院数学所，师从王光寅研究员和丁伟岳；1991年北京大学数学系博士后出站，合作导师张恭庆。马力教授主要从事几何分析和非线性分析、偏微分方程的研究。近期在黎曼几何的重要问题比如Yamabe流、Ricci流等方面取得了一系列重要的研究成果。在Adv. Math., J. Math. Pures Appl., Arch. Ration. Mech. Anal., J. Funct. Anal., JDE, Comm. Math. Phy., CVPDE等著名学术期刊上发表多篇论文。长期担任了两个国际数学sci杂志(AGAG, JPDOA)编委。

邀请人：非线性分析与PDE团队