Sliding methods for fractional parabolic equations


主讲人:Chen Wenxiong,纽约Yeshiva大学终身教授




主讲人介绍:Chen Wenxiong,美国纽约Yeshiva大学终身教授,数学系主任,国际知名的数学家。曾多次获得美国国家科学基金奖。担任Nonlinear Analysis: Theory, Methods & Applications 及Communications on Pure and Applied Analysis 两个SCI数学杂志的编辑。研究方向为非线性偏微分方程,目前以分数阶Laplace方程为主。Chen教授在数学顶级期刊Annals of Math, J. of Diff. Geom., Comm. Pure and Appl. Math, Duke Math. J, Advance in Math, Arch. Rat. Mech. Anal.等发表论文80余篇,并出版了三本专著,他引已达五千余次,其中在Duke Math. J.上发表的名为Classification of solutions of some nonlinear elliptic equations的论文被引高达1000余次。

内容介绍: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.