云师范大学数学学院学术报告

题目：Qualitative properties of solutions for nonlinear fractional parabolic equations

报告人：陈文雄  美国纽约Yeshiva大学终身教授

时间： 2022年4月22日上午08:30-10:00

腾讯会议：155-398-042

https://meeting.tencent.com/dm/Y2rBc6LmdQe4

Abstract: In this talk, I will summarize our recent results on the qualitative properties of positive solutions for nonlinear parabolic fractional equations

                                        (1)

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 references below.)

There have been a series of results for equation (1) if the fractional Laplacian  is replaced by the regular Laplacian . However due to the non-locality of the fractional operator, many traditional approaches 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 useful 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, Adv. Nonlinear Stud. 21 (2021), 939–958.

[3] W. Chen, L. Wu, and P. Wang, Nonexistence of solutions for indefinite fractional parabolic equations, Adv. Math. 392 (2021), Paper No. 108018

报告人简介：陈文雄，教授，博士生导师。美国纽约Yeshiva大学终身教授，数学系主任，南开大学特聘讲座教授（天津市千人），国际知名的数学家，研究领域包括非线性偏分方程、几何分析、非线性泛函分析等。 曾多次获得美国国家科学基金奖。担任Nonlinear Analysis: Theory, Methods & Applications 和“Communication on Pure and Applied Analysis”的编委。在数学顶级期刊Annals of Math, J. Diff. Geom,  Comm. Pure and Appl. Math,  Duke Math.  J, Adv. Math,  Arch. Rat. Mech.Anal,  J. Diff. Equ, Trans. AMS等发表论文60余篇，其中与Congming Li教授合作发表在Duke Math. J.上的文章“Classification of solutions of some nonlinear elliptic equations”引用高达750次以上。出版学术专著《Methods on Nonlinear Elliptic Equations》与《The Fractional Laplacian》。