Differential Harnack estimates for a nonlinear heat equation

被引：43

作者：

Cao, Xiaodong ^{[1
]}

Ljungberg, Benjamin Fayyazuddin ^{[2
]}

Liu, Bowei ^{[3
]}

机构：

[1] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

[2] Cornell Univ, Ithaca, NY 14853 USA

[3] Princeton Univ, Princeton, NJ 08544 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2013年 / 265卷 / 10期

基金：

美国国家科学基金会;

关键词：

Differential Harnack inequality; RIEMANNIAN-MANIFOLDS; INEQUALITIES;

D O I：

10.1016/j.jfa.2013.07.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider positive solutions to the semilinear heat equation w(t) = Delta w aw log w, a not equal 0, on complete Riemannian manifolds without boundary. This equation has applications to studying Ricci flow and gradient Ricci solitons. We derive several differential Hamack inequalities which improve on those of Y. Yang (2008) [13]. We use these inequalities to derive bounds on gradient Ricci solitons. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：2312 / 2330

页数：19

共 13 条

[1] Differential Harnack estimates for backward heat equations with potentials under the Ricci flow [J].