Hamilton-Souplet-Zhang’s Gradient Estimates for Two Types of Nonlinear Parabolic Equations under the Ricci Flow

Hamilton-Souplet-Zhang’s Gradient Estimates for Two Types of Nonlinear Parabolic Equations under the Ricci Flow

We consider gradient estimates for two types of nonlinear parabolic equations under the Ricci flow: one is the equation ut=Δu+aulog⁡u+bu with a,b being two real constants; the other is ut=Δu+λuα with λ,α being two real constants. By a suitable scaling for the above two equations, we obtain Hamilton-...

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Main Authors: Guangyue Huang, Bingqing Ma
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2016/2894207
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spelling doaj-5ad7c979bb6b4517be73aecdc6c1c1902020-11-24T23:44:22ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/28942072894207Hamilton-Souplet-Zhang’s Gradient Estimates for Two Types of Nonlinear Parabolic Equations under the Ricci FlowGuangyue Huang0Bingqing Ma1College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, ChinaHenan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, ChinaWe consider gradient estimates for two types of nonlinear parabolic equations under the Ricci flow: one is the equation ut=Δu+aulog⁡u+bu with a,b being two real constants; the other is ut=Δu+λuα with λ,α being two real constants. By a suitable scaling for the above two equations, we obtain Hamilton-Souplet-Zhang-type gradient estimates.http://dx.doi.org/10.1155/2016/2894207
collection DOAJ
language English
format Article
sources DOAJ
author Guangyue Huang
Bingqing Ma
spellingShingle Guangyue Huang
Bingqing Ma
Hamilton-Souplet-Zhang’s Gradient Estimates for Two Types of Nonlinear Parabolic Equations under the Ricci Flow
Journal of Function Spaces
author_facet Guangyue Huang
Bingqing Ma
author_sort Guangyue Huang
title Hamilton-Souplet-Zhang’s Gradient Estimates for Two Types of Nonlinear Parabolic Equations under the Ricci Flow
title_short Hamilton-Souplet-Zhang’s Gradient Estimates for Two Types of Nonlinear Parabolic Equations under the Ricci Flow
title_full Hamilton-Souplet-Zhang’s Gradient Estimates for Two Types of Nonlinear Parabolic Equations under the Ricci Flow
title_fullStr Hamilton-Souplet-Zhang’s Gradient Estimates for Two Types of Nonlinear Parabolic Equations under the Ricci Flow
title_full_unstemmed Hamilton-Souplet-Zhang’s Gradient Estimates for Two Types of Nonlinear Parabolic Equations under the Ricci Flow
title_sort hamilton-souplet-zhang’s gradient estimates for two types of nonlinear parabolic equations under the ricci flow
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2016-01-01
description We consider gradient estimates for two types of nonlinear parabolic equations under the Ricci flow: one is the equation ut=Δu+aulog⁡u+bu with a,b being two real constants; the other is ut=Δu+λuα with λ,α being two real constants. By a suitable scaling for the above two equations, we obtain Hamilton-Souplet-Zhang-type gradient estimates.
url http://dx.doi.org/10.1155/2016/2894207
work_keys_str_mv AT guangyuehuang hamiltonsoupletzhangsgradientestimatesfortwotypesofnonlinearparabolicequationsunderthericciflow
AT bingqingma hamiltonsoupletzhangsgradientestimatesfortwotypesofnonlinearparabolicequationsunderthericciflow
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