北航数学论坛学术报告
Qualitative properties of solutions for nonlinear fractional parabolic equations
陈文雄 教授
（Yeshiva大学）
报告时间：上午8：30-9：30，2021年8月16日、18日、20日
报告地点： 腾讯会议ID：656 240 356 (8月16日)、974 711 053（8月18日）、606 293 726（8月20日）
密码：123456
腾讯会议链接：https://meeting.tencent.com/dm/u7E9vEUyORDv (8月16日)
https://meeting.tencent.com/dm/IVfRSjn3ma69 （8月18日）
https://meeting.tencent.com/dm/hCwLikNAtXe9 （8月20日）
内容简介：In this series of talks, we will summarize our recent developments on the qualitative properties of positive solutions for nonlinear parabolic fractional equations
We will mainly consider the following three situations.
1) The asymptotic symmetry of solutions in a unit ball and in the whole
space [1],
2) the monotonicity of the entire solutions in half spaces [2], and
3) the non-existence of entire solutions with indefinite non-linearity 
[3].
(Please see the corresponding papers below.)
Due to the presence of senior undergraduate and junior graduate students, we will try to make the first talk as elementary as possible, so that the students with calculus background can follow easily.
There have been a series of results for equation (1) if the fractional Laplacian 
is replaced by the regular Laplacian 
.
Due to the non-locality of the fractional operator, many traditional ap[1]
proaches do not work anymore. We have introduced several new ideas and developed a series of techniques to deal with the fractional cases. We believe that these new techniques will become effective tools in solving a variety of other nonlocal problems.
References
[1] W. Chen, P. Wang, Y. Niu, and Y. Hu, Asymptotic method of moving
planes for fractional parabolic equations, Adv. Math, 2020.
[2] W. Chen and L. Wu, Liouville theorems for fractional parabolic
equations, submitted to CVPDE, 2021.
[3] W. Chen, L. Wu, and P. Wang, Nonexistence of solutions for indefinite fractional parabolic equations, accepted by Adv. Math. 2021.
报告人简介：陈文雄，Yeshiva大学数学系终身教授，南开大学特聘讲座教授（天津市级人才），曾多次获得美国国家科学基金奖，致力于研究非线性偏微分方程、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。发表论文80余篇，发表在Ann. of Math.、Duke Math. J.、CPAM、JDG、Adv. Math.、ARMA等国际著名数学期刊上，他引超过5000次。
邀请人：戴蔚
