Gradient estimates and Liouville theorems for nonlinear parabolic equations on noncompact Riemannian manifolds

doi:10.1016/j.na.2011.05.008

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	Gradient estimates and Liouville theorems for nonlinear parabolic equations on noncompact Riemannian manifolds
	Zhu, Xiaobao
	2011-10-01
发表期刊	NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
ISSN	0362-546X
卷号	74 期号:15 页码:5141-5146
摘要	Let M be a complete noncompact Riemannian manifold. In this paper, we derive a local gradient estimate for positive solutions of the nonlinear parabolic equation. (Delta - partial derivative/t) u(x, t) + lambda(x, t)u(alpha) (x, t) = 0 on M x (-infinity, 0]. We also obtain a theorem of Liouville type for positive solutions of this nonlinear equation. This paper extends the result of Souplet and Zhang [P. Souplet, Qi S. Zhang, Sharp gradient estimate and Yau's Liouville theorem for the heat equation on noncompact manifolds, Bull. Lond. Math. Soc. 38 (2006) 1045-1053]. (C) 2011 Elsevier Ltd. All rights reserved.
关键词	Gradient estimates Nonlinear parabolic equations Liouville theorems
DOI	10.1016/j.na.2011.05.008
语种	英语
资助项目	NSFC[11001268]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000291471000022
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12739
专题	中国科学院数学与系统科学研究院
通讯作者	Zhu, Xiaobao
作者单位	Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhu, Xiaobao. Gradient estimates and Liouville theorems for nonlinear parabolic equations on noncompact Riemannian manifolds[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2011,74(15):5141-5146.
APA	Zhu, Xiaobao.(2011).Gradient estimates and Liouville theorems for nonlinear parabolic equations on noncompact Riemannian manifolds.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,74(15),5141-5146.
MLA	Zhu, Xiaobao."Gradient estimates and Liouville theorems for nonlinear parabolic equations on noncompact Riemannian manifolds".NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 74.15(2011):5141-5146.