GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LINEAR AND NONLINEAR PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS

被引：0

作者：

朱晓宝 ^{[1
]}

机构：

[1] Department of Mathematics, School of Information, Renmin University of China

来源：

Acta Mathematica Scientia | 2016年 / 02期

基金：

美国国家科学基金会;

关键词：

Gradient estimate; linear parabolic equation; nonlinear parabolic equation; Liouville type theorem;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In this article, we will derive local elliptic type gradient estimates for positive solutions of linear parabolic equations(?-?/(?t))u(x, t) + h(x,t)u(x,t) = 0 and nonlinear parabolic equations(?-?-/(?t))u(x,t) + h(x, t)u~p(x,t) = 0(p > 1) on Riemannian manifolds.As applications, we obtain some theorems of Liouville type for positive ancient solutions of such equations. Our results generalize that of Souplet-Zhang([1], Bull. London Math. Soc.38(2006), 1045-1053) and the author([2], Nonlinear Anal. 74(2011), 5141-5146).

引用

页码：514 / 526

页数：13

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