Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow
Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow
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DOI：
10.2140/pjm.2012.257.199
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发表时间：
2010-09
影响因子：
0.6
通讯作者：
Jia-Yong Wu
中科院分区：
文献类型：
--
作者：
Jia-Yong Wu
我们证明，对于具有不同电位的非线性向后热方程式的阳性溶液和RICCI流动的阳性解决方案。我们还在封闭的表面上得出了$ \ varepsilon $ -RICCI流动下的非线性热方程的插值harnack不等式。这些新的Harnack不等式扩展了先前的差异harnack不等式的线性热方程，并在RICCI流下具有电势。
We prove several differential Harnack inequalities for positive solutions to nonlinear backward heat equations with different potentials coupled with the Ricci flow. We also derive an interpolated Harnack inequality for the nonlinear heat equation under the $\varepsilon$-Ricci flow on a closed surface. These new Harnack inequalities extend the previous differential Harnack inequalities for linear heat equations with potentials under the Ricci flow.