| 摘要: |
| 本文通过Li-Yau梯度估计的方法和Jun Sun对热方程在一般几何流下梯度估计的研究，推导出一类重要的非线性抛物方程在一般几何流演化下的梯度估计，并得到了哈拿克不等式等一些结论.推广了Wang的结果. |
| 关键词: 梯度估计 几何流 一种非线性抛物方程 哈拿克不等式 |
| DOI： |
| 分类号:O186.1 |
| 基金项目: |
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| GRADIENT ESTIMATE FOR A NONLINEAR PARABOLIC EQUATION UNDER GEOMETRIC FLOW |
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WU Meng-fei
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School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
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| Abstract: |
| In this paper, through the Li-Yau gradient estimate and Jun Sun's research on the gradient estimate of heat equation under general geometric flow, we will derive local gradient estimates for positive solutions of a nonlinear parabolic equation on Riemannian manifold under general geometric flow. These results can be regarded as a generlization of Wang's results. At the same time, we give a corresponding Harnack inequality. |
| Key words: gradient estimate geometric flow a nonlinear parabolic equation Harnack inequality |
