报 告 人：陈文雄 教授
报告题目：Liouville Theorems for Fractional Parabolic Equations
报告时间：2021年11月13-14日（周六、日）上午9:30
报告地点：腾讯会议（ID：287138845（13日），347466203（14日） ）
报告人简介：
陈文雄，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NonlinearAnalysis: 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。
他曾先后在如下的SCI一区数学期刊上发表3篇论文：Annals of Mathematics: 1 篇，Communications of Pure and Applied Mathematics: 2 篇。
根据 GoogleScholar，他在1991 年Duke Math. J.上发表的名为 Classification of solutions of some nonlinear elliptic equations 一篇被引高达 750次以上。在 2006年 CPAM 上发表的名为Classification for the solutions of integral equations 一篇被引高达 400 次以上。
近年来，他在Advances in Mathematics 发表的文章中有三篇被列为高被引（Highly Cited).出版专著《Methods on Nonlinear EllipticEquations》一本。即将出版另一本专著《The Fractional Laplacian》。
报告摘要：
We establish several Liouville type theorems for entire solutions tofractional parabolic equations. We first obtain the key ingredients needed inthe proof of Liouville theorems, such as narrow region principles and maximumprinciples for antisymmetric functions in unbounded domains, in which weremarkably weaken the usual decay condition u → 0 at infinity to a polynomialgrowth on u by constructing proper auxiliary functions. Then we derivemonotonicity for the solutions in a half space ℝn+× ℝandobtain some new connections between the nonexistence of solutions in a halfspace ℝn+× ℝand inthe whole space ℝn−1 × ℝandtherefore prove the corresponding Liouville type theorems. To overcome thedifficulty caused by the nonlocality of the fractional Laplacian, we introduceseveral new ideas which will become useful tools in investigating qualitativeproperties of solutions for a variety of nonlocal parabolic problems.