Method of moving planes for fractional parabolic equations

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

時(shí)間：2024年7月2日9：30

地點(diǎn)：三號(hào)樓332室

舉辦單位：數(shù)理學(xué)院

主講人介紹：Chen Wenxiong，美國(guó)紐約Yeshiva大學(xué)終身教授，數(shù)學(xué)系主任，國(guó)際知名的數(shù)學(xué)家。曾多次獲得美國(guó)國(guó)家科學(xué)基金獎(jiǎng)。擔(dān)任Nonlinear Analysis: Theory, Methods & Applications 及Communications on Pure and Applied Analysis 兩個(gè)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(jí)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(zhuān)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 method of moving planes for nonlinear fractional parabolic equations ?_t u+〖(-?)〗^s u=f(t,u(x,t)). We will prove narrow region principles, both asymptotic and for entire solutions. Then we will apply the method of moving planes to prove the radial symmetry and monotonicity of positive solutions to such equations in a unit ball and the monotonicity of solutions on a half space. We will illustrate how to modify the methods and estimates on elliptic problems so that they can be applied to parabolic problems.