Gradient Estimates for a Nonlinear Heat Equation on Compact Riemannian Manifold  

作　　者：Xinrong JIANG Caisheng LIAO 

机构地区：[1]Institute of Mathematics and Information Science, Jiangxi Normal University, Jiangxi 330022, P. R. China [2]Department of Mathematics, East China Normal University, Shanghai 200241, P. R. China

出　　处：《Journal of Mathematical Research with Applications》2012年第6期743-753,共11页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos. 10871069; 11261038);Shanghai Leading Academic Discipline Project (Grant No. B407)

摘　　要：In this paper, we study gradient estimates for the nonlinear heat equation ut-△u = au log u, on compact Riemannian manifold with or without boundary. We get a Hamilton type gradient estimate for the positive smooth solution to the equation on close manifold, and obtain a Li-Yau type gradient estimate for the positive smooth solution to the equation on compact manifold with nonconvex boundary.In this paper, we study gradient estimates for the nonlinear heat equation ut-△u = au log u, on compact Riemannian manifold with or without boundary. We get a Hamilton type gradient estimate for the positive smooth solution to the equation on close manifold, and obtain a Li-Yau type gradient estimate for the positive smooth solution to the equation on compact manifold with nonconvex boundary.

关 键 词：nonlinear heat equation Riemannian manifold gradient estimates 

分 类 号：O551.3[理学—热学与物质分子运动论] O186.12[理学—物理]