加权黎曼流形上加权非线性反应扩散方程的微分Harnack估计  

DIFFERENCE HARNACK ESTIMATES FOR WEIGHTED NONLINEAR REACTION-DIFFUSION EQUATIONS ON WEIGHTED RIEMANNIAN MANIFOLDS

作　　者：王宇钊 王雪明 WANG Yu-zhao;WANG Xue-ming(School of Mathematical Sciences,Shanxi University,Taiyuan 030006 China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《数学杂志》2020年第6期653-661,共9页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11701347);Natural Science Foundation of Shanxi Province(201901D211185).

摘　　要：本文研究了黎曼流形上的微分Harnack估计问题.利用最大值原理和加权的p-Bochner公式的方法,在CD(0,N)条件下,获得了加权黎曼流形上加权非线性反应扩散方程的Li-Yau型和Hamilton型微分Harnack估计,推广了作者在不加权时非负Ricci曲率条件下成立的结果.In this paper, we study the problem of difference Harnack estimate on Riemannian manifolds. By using maximum principle and weighted p-Bochner formula, we derive the Li-Yau type difference Harnack estimate and Hamilton type estimate for the positive solutions to weighted nonlinear reaction-diffusion equation on compact weighted Riemannian manifold with curvature dimension condition CD(0, N), which generalizes the non-weighted case under the condition of nonnegative Ricci curvature.

关 键 词：加权反应扩散方程 Li-Yau估计 Hamilton估计 曲率维数条件 Bochner公式 

分 类 号：O175.29[理学—数学]