Method of moving planes for fractional parabolic equations

主讲人：Chen Wenxiong，纽约Yeshiva大学终身教授

时间：2024年7月2日9：30

地点：三号楼332室

举办单位：数理学院

主讲人介绍：Chen Wenxiong，美国纽约Yeshiva大学终身教授，数学系主任，国际知名的数学家。曾多次获得美国国家科学基金奖。担任Nonlinear Analysis: Theory, Methods & Applications 及Communications on Pure and Applied Analysis 两个SCI数学杂志的编辑。研究方向为非线性偏微分方程，目前以分数阶Laplace方程为主。Chen教授在数学顶级期刊Annals of Math, J. of Diff. Geom., Comm. Pure and Appl. Math, Duke Math. J, Advance in Math, Arch. Rat. Mech. Anal.等发表论文80余篇，并出版了三本专著，他引已达五千余次，其中在Duke Math. J.上发表的名为Classification of solutions of some nonlinear elliptic equations的论文被引高达1000余次。

内容介绍：In this talk, we will introduce the method of moving planes for nonlinear fractional parabolic equations ∂_t u+〖(-∆)〗^s u=f(t,u(x,t)). We will prove narrow region principles, both asymptotic and for entire solutions. Then we will apply the method of moving planes to prove the radial symmetry and monotonicity of positive solutions to such equations in a unit ball and the monotonicity of solutions on a half space. We will illustrate how to modify the methods and estimates on elliptic problems so that they can be applied to parabolic problems.