一种非线性抛物方程在一般几何流下的梯度估计  

GRADIENT ESTIMATE FOR A NONLINEAR PARABOLIC EQUATION UNDER GEOMETRIC FLOW

作　　者：仵孟飞 WU Meng-fei(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2022年第4期287-299,共13页Journal of Mathematics

摘　　要：本文通过Li-Yau梯度估计的方法和Jun Sun对热方程在一般几何流下梯度估计的研究,推导出一类重要的非线性抛物方程在一般几何流演化下的梯度估计,并得到了哈拿克不等式等一些结论.推广了Wang的结果.In this paper,through the Li-Yau gradient estimate and Jun Sun’s research on the gradient estimate of heat equation under general geometric flow,we will derive local gradient estimates for positive solutions of a nonlinear parabolic equation on Riemannian manifold under general geometric flow.These results can be regarded as a generlization of Wang’s results.At the same time,we give a corresponding Harnack inequality.

关 键 词：梯度估计 几何流 一种非线性抛物方程 哈拿克不等式 

分 类 号：O186.1[理学—数学]