Sliding methods for fractional parabolic equations

主講人：Chen Wenxiong，紐約Yeshiva大學(xué)終身教授

時間：2024年7月3日9：30

地點(diǎn)：三號樓332室

舉辦單位：數(shù)理學(xué)院

主講人介紹：Chen Wenxiong，美國紐約Yeshiva大學(xué)終身教授，數(shù)學(xué)系主任，國際知名的數(shù)學(xué)家。曾多次獲得美國國家科學(xué)基金獎。擔(dān)任Nonlinear Analysis: Theory, Methods & Applications 及Communications on Pure and Applied Analysis 兩個SCI數(shù)學(xué)雜志的編輯。研究方向?yàn)榉蔷€性偏微分方程，目前以分?jǐn)?shù)階Laplace方程為主。Chen教授在數(shù)學(xué)頂級期刊Annals of Math, J. of Diff. Geom., Comm. Pure and Appl. Math, Duke Math. J, Advance in Math, Arch. Rat. Mech. Anal.等發(fā)表論文80余篇，并出版了三本專著，他引已達(dá)五千余次，其中在Duke Math. J.上發(fā)表的名為Classification of solutions of some nonlinear elliptic equations的論文被引高達(dá)1000余次。

內(nèi)容介紹：In this talk, we will introduce the sliding method for nonlinear fractional parabolic equations?_t u+〖(-?)〗^s u=f(t,u(x,t)). We will prove a maximum principle for unbounded regions by using a generalized weighted average inequality, then we will use it to derive the monotonicity of solutions in the whole space in x_n direction and its 1-dimensional symmetry. We will apply the sliding method to obtain other results. We will illustrate how to modify the methods and estimates on elliptic problems so that they can be applied to parabolic problems.