报 告 人：陈文雄教授
报告题目：Liouville Theorems forFractional Parabolic Equations
报告时间：2021年11月20日（周六）上午9:30
报告地点：腾讯会议（ID：359 124 808）
主办单位：数学与统计学院、科学技术研究院
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：Annalsof Mathematics: 1 篇，Communicationsof Pure and Applied Mathematics: 2 篇。根据 GoogleScholar，他在1991年DukeMath. J.上发表的名为 Classificationof 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Classificationfor the solutions of integral equations 一篇被引高达400 次以上。
近年来，他在Advancesin Mathematics 发表的文章中有三篇被列为高被引（HighlyCited).出版专著《Methods onNonlinear Elliptic Equations》一本。即将出版另一本专著《The FractionalLaplacian》。
报告摘要：
Weestablish several Liouville type theorems for entire solutions to fractionalparabolic equations. We first obtain the key ingredients needed in the proof ofLiouville theorems, such as narrow region principles and maximum principles forantisymmetric functions in unbounded domains, in which we remarkably weaken theusual decay condition u → 0 at infinity to a polynomial growth on u byconstructing proper auxiliary functions. Then we derive monotonicity for thesolutions 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.
邀 请 人：吕中学