Li-Yau Estimates for a Nonlinear Parabolic Equation on Manifolds

被引：16

作者：

Zhu, Xiaorui ^{[1
,2
]}

Li, Yi ^{[3
,4
]}

机构：

[1] China Maritime Police Acad, Ningbo 315801, Peoples R China

[2] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

[3] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[4] Fudan Univ, Shanghai Ctr Math Sci, Shanghai 200433, Peoples R China

来源：

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2014年 / 17卷 / 3-4期

关键词：

Nonlinear parabolic equation; Li-Yau estimates; RIEMANNIAN-MANIFOLDS; RICCI FLOW;

D O I：

10.1007/s11040-014-9155-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we derive Li-Yau gradient estimates for the positive solution of a nonlinear parabolic equation u(t) = Delta u-qu-au(ln u)(alpha), where q is a C-2 function and a, alpha are constants, on a complete manifold (M, g) with bounded below Ricci curvature. The results generalize classical Li-Yau gradient estimates and some recent works on this direction.

引用

页码：273 / 288

页数：16

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