Hamilton-type gradient estimates for a nonlinear parabolic equation on Riemannian manifolds

被引：12

作者：

Qian, Bin ^{[1
,2
]}

机构：

[1] Changshu Inst Technol, Dept Math, Changshu 215500, Peoples R China

[2] Univ Toulouse, CNRS, Inst Math Toulouse, F-5219 Toulouse, France

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2011年 / 27卷 / 06期

关键词：

Nonlinear parabolic equations; Li-Yau inequalities; Harnack differential inequalities; gradient estimates;

D O I：

10.1007/s10114-011-8474-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (M,g) be a complete noncompact Riemannian manifold. In this note, we derive a local Hamilton-type gradient estimate for positive solution to a simple nonlinear parabolic equation partial derivative tu - Delta u + au log u + qu on M x (0,a), where a is a constant and q is a C (2) function. This result can be compared with the ones of Ma (JFA, 241, 374-382 (2006)) and Yang (PAMS, 136, 4095-4102 (2008)). Also, we obtain Hamilton's gradient estimate for the Schodinger equation. This can be compared with the result of Ruan (JGP, 58, 962-966 (2008)).

引用

页码：1071 / 1078

页数：8

共 12 条

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[2]

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[3]

Bakry D, 2009, POTENTIAL THEORY AND STOCHASTICS IN ALBAC: AUREL CORNEA MEMORIAL VOLUME, CONFERENCE PROCEEDINGS, P1

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