Gradient estimates and Liouville theorems for nonlinear parabolic equations on noncompact Riemannian manifolds
文献类型：期刊论文
| 作者 | Zhu, Xiaobao |
| 刊名 | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
 |
| 出版日期 | 2011-10-01 |
| 卷号 | 74期号:15页码:5141-5146 |
| 关键词 | Gradient estimates Nonlinear parabolic equations Liouville theorems |
| ISSN号 | 0362-546X |
| DOI | 10.1016/j.na.2011.05.008 |
| 英文摘要 | 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. |
| 语种 | 英语 |
| WOS记录号 | WOS:000291471000022 |
| 出版者 | PERGAMON-ELSEVIER SCIENCE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/12738]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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