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Asymptotic method of moving planes for fractional parabolic equations


报告人: 陈文雄 教授



报告地点: Zoom 会议


会议 ID:597 651 2470



陈文雄教授现任美国叶史瓦大学数学系终身教授,叶史瓦大学数学系主任, 国际数学期刊 Nonlinear AnalysisSeries A, Theory and Applications Communication on Pure and Applied Analysis 的编辑。陈文雄教授是偏微分方程和几何分析的杰出专家,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。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 已被引用达500余次。


In this series of lectures, we will consider nonlinear parabolic fractional equations. we develop a systematical approach in applying an asymptotic method of moving planes to investigate qualitative properties of positive solutions for fractional parabolic equations. We first obtain a series of needed key ingredients such as narrow region principles, and various asymptotic maximum and strong maximum principles for antisymmetric functions in both bounded and unbounded domains. Then we illustrate how this new method can be employed to obtain asymptotic radial symmetry and monotonicity of positive solutions in a unit ball and on the whole space. Namely, we show that no matter what the initial data are, the solutions will eventually approach to radially symmetric functions. We firmly believe that the ideas and methods introduced here can be conveniently applied to study a variety of nonlocal parabolic problems with more general operators and more general nonlinearities.


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