Gradient estimates for a nonlinear parabolic equation on complete non-compact Riemannian manifolds

被引：60

作者：

Chen, Li ^{[1
]}

Chen, Wenyi ^{[1
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2009年 / 35卷 / 04期

关键词：

Nonlinear parabolic equation; Gradient estimate; Positive solution;

D O I：

10.1007/s10455-008-9141-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we derive a local gradient estimate for the positive solution to the following parabolic equation u(t) = Delta u + au log u + bu in M, where a, b are real constants, M is a complete noncompact Riemannian manifold. As a corollary, we give a local gradient estimate for the corresponding elliptic equation: Delta u + au log u + bu = 0 in M, which improves and extends the result of Ma (J Funct Anal 241: 374-382, 2006) and get a bound for the positive solution to this elliptic equation.

引用

页码：397 / 404

页数：8

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