Gradient Estimates and Harnack Inequality for a Nonlinear Parabolic Equation on Complete Manifolds  

作　　者：Jiaxian Wu Yi-Hu Yang 

机构地区：[1]Department of Mathematics,Tongji University,Shanghai 200092,China [2]Department of Mathematics,Shanghai Jiao Tong University,Shanghai 200240,China

出　　处：《Communications in Mathematics and Statistics》2013年第4期437-464,共28页数学与统计通讯（英文）

基　　金：Supported partially by NSF of China(No.11171253).

摘　　要：Let M be a noncompact complete Riemannian manifold.In this paper,we consider the following nonlinear parabolic equation on M ut(x,t)=△u(x,t)+au(x,t)ln u(x,t)+bu^α(x,t).We prove a Li–Yau type gradient estimate for positive solutions to the above equation;as an application,we also derive the corresponding Harnack inequality.These results generalize the corresponding ones proved by Li(J Funct Anal 100:233–256,1991).

关 键 词：Gradient estimate Ricci curvature Harnack inequality Nonlinear parabolic equation 

分 类 号：O17[理学—数学]