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| 摘要: |
| 本文研究了多孔介质方程在一般几何流下的梯度估计.通过Aroson和Bénilan对多孔介质方程的研究结果以及运用Li-Yau梯度估计的方法，获得了对多孔介质方程的正解对于Laplace算子以及drifing Laplace算子在一般几何流演化下的一些梯度估计，推广了Zhu Xiao-bao和Deng Yi-hua的结果. |
| 关键词: 梯度估计 几何流 多孔介质方程 哈拿克不等式 |
| DOI： |
| 分类号:O186.1 |
| 基金项目: |
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| GRADIENT ESTIMATE FOR POSITIVE SOLUTIONS OF THE PME UNDER GEOMETRIC FLOW |
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ZHAO He-lei
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| Abstract: |
| In this paper, we derive a local gradient estimate of the Aronson-Bénilan type with Laplace operator and drifting Laplace operator for positive solutions of porous medium equations posed on Riemainnian manifolds with bounded symmetric tensor by using Li-Yau method. These results extend Zhu Xiao-bao's and Deng Yi-hua's results. |
| Key words: gradient estimate geometric flow porous medium equations Harnack inequality |
