| Gradient Estimates for a Nonlinear Heat Equation on Compact Riemannian Manifold |
| Received:January 20, 2011 Revised:March 27, 2012 |
| Key Words:
nonlinear heat equation Riemannian manifold gradient estimates.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10871069; 11261038) and Shanghai Leading Academic Discipline Project (Grant No.B407). |
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| Abstract: |
| In this paper, we study gradient estimates for the nonlinear heat equation $u_t-\triangle u=au\log u$, 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2012.06.014 |
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