| 摘要: |
| 本文研究了黎曼流形上的微分Harnack估计问题.利用最大值原理和加权的p-Bochner公式的方法，在CD（0，N）条件下，获得了加权黎曼流形上加权非线性反应扩散方程的Li-Yau型和Hamilton型微分Harnack估计，推广了作者在不加权时非负Ricci曲率条件下成立的结果. |
| 关键词: 加权反应扩散方程 Li–Yau估计 Hamilton估计 曲率维数条件 Bochner公式 |
| DOI： |
| 分类号:O175.29 |
| 基金项目:Supported by National Natural Science Foundation of China (11701347); Natural Science Foundation of Shanxi Province (201901D211185). |
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| DIFFERENCE HARNACK ESTIMATES FOR WEIGHTED NONLINEAR REACTION-DIFFUSION EQUATIONS ON WEIGHTED RIEMANNIAN MANIFOLDS |
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WANG Yu-zhao, WANG Xue-ming
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School of Mathematical Sciences, Shanxi University, Taiyuan 030006 China
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| Abstract: |
| In this paper, we study the problem of difference Harnack estimate on Riemannian manifolds. By using maximum principle and weighted p-Bochner formula, we derive the Li-Yau type difference Harnack estimate and Hamilton type estimate for the positive solutions to weighted nonlinear reaction-diffusion equation on compact weighted Riemannian manifold with curvature dimension condition CD(0, N), which generalizes the non-weighted case under the condition of nonnegative Ricci curvature. |
| Key words: weighted nonlinear reaction diffusion equation Li-yau type difference Harnack estimate hamilton type difference Harnack estimate curvature dimension condition weighted p-Bochner formula |
