Hamilton-Souplet-Zhang's gradient estimates for two weighted nonlinear parabolic equations  

作　　者：MA Bing-qing HUANG Guang-yue 

机构地区：[1]Department of Mathematics, Henan Normal University, Xinxiang 453007, China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2017年第3期353-364,共12页高校应用数学学报（英文版）（B辑）

基　　金：Supported by NSFC(11371018,11401179,11671121)

摘　　要：In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded below: One is $${u_t} = {\Delta _f}u + au\log u + bu$$ with a, b two real constants, and another is $${u_t} = {\Delta _f}u + \lambda {u^\alpha }$$ with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f.In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded below: One is $${u_t} = {\Delta _f}u + au\log u + bu$$ with a, b two real constants, and another is $${u_t} = {\Delta _f}u + \lambda {u^\alpha }$$ with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f.

关 键 词：Hamilton’s gradient estimate Souplet-Zhang’s gradient estimate weighted nonlinear parabolic equation Bakry-Émery Ricci tensor 

分 类 号：O175.26[理学—数学] O186.12[理学—基础数学]