报告题目1：Direct method on fractional equations

报告人：陈文雄教授，Yeshiva大学

报告时间：2024年7月2日（周二）15:00-17:00

报告地点：20-306

报告摘要：In this talk, we summarize some of the recent developments in the area of fractional equations with focus on the ideas and direct methods on fractional non-local operators. These results have more or less appeared in a series of previous literatures, in which the ideas were usually submerged in detailed calculations. What we are trying to do here is to single out these ideas and illustrate the inner connections among them, so that the readers can see the whole picture and quickly grasp the essence of these useful methods and apply them to a variety of problems in this area.

报告题目2：Moving planes and sliding methods for fractional elliptic and parabolic equations

报告人：陈文雄教授，Yeshiva大学

报告时间：2024年7月3日（周三）15:00-17:00

报告地点：20-306

报告摘要：In this talk, we summarize some of the recent developments in the area of fractional elliptic and parabolic equations with focus on how to apply the sliding method and the method of moving planes to obtain qualitative properties of solutions. We will compare the two methods and point out the pros and cons of each. We will demonstrate how to modify the ideas and techniques in studying fractional elliptic equations and then to employ them to investigate fractional parabolic problems. Besides deriving monotonicity of solutions, some other applications of the sliding method will be illustrated.

报告题目3：SOME RECENT DEVELOPMENTS ON FRACTIONAL PARABOLIC EQUATIONS

报告人：陈文雄教授，Yeshiva大学

报告时间：2024年7月4日（周四）9:00-11:00

报告地点：20-306

报告摘要：In this talk, I will summarize some of our recent results on the qualitative properties of positive solutions for nonlinear parabolic fractional equations. including asymptotic radial symmetry of solutions, monotonicity of the entire solutions in half spaces, non-existence of entire solutions with indenite non-linearities, radial symmetry of ancient solutions in the whole space, and sliding method for fractional parabolic equations. We have introduced several new ideas and developed a series of new techniques to deal with the fractional cases. We believe that these new tools can be applied to solve many other nonlocal problems, both elliptic and parabolic.

报告人简介：陈文雄，教授，博士生导师，Yeshiva大学数学系终身教授，南开大学特聘讲座教授。曾多次获得美国国家科学基金奖，致力于偏微分方程、非线性泛函分析和几何分析等。研究方向主要包括：非线性偏微分方程正解的分类，几何不等式和黎曼流形上正解的性质等。论文发表在Annals of Math, J. of Diff. Geom, Comm. Pure and Appl. Math, Duke Math. J, Advances in Math, Arch. Rat. Mech. Anal等著名国际数学期刊，他引已达五千余次。

邀请人：非线性分析与PDE团队