Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds

Nguyen Ngoc Khanh

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Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds

机译：黎曼流形上一般热方程的Li Yau型梯度估计。

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In this paper, we consider gradient estimates on complete noncompact Riemannian manifolds $(M,g)$ for the following general heat equation [ u_t=Delta _V u+aulog u+bu ] where $a$ is a constant and $b$ is a differentiable function defined on $Mimes [0, infty )$. We suppose that the Bakry-émery curvature and the $N$-dimensional Bakry-émery curvature are bounded from below, respectively. Then we obtain the gradient estimate of Li-Yau type for the above general heat equation. Our results generalize the work of Huang-Ma ([4]) and Y.?Li ([6]), recently.

机译：在本文中，我们考虑以下一般热方程 [u_t = Delta _V u + au log u + bu ]的完全非紧黎曼流形$（M，g）$的梯度估计，其中$ a $是一个常数$ b $是在$ M times [0， infty）$上定义的可微函数。我们假设Bakry-émery曲率和$ N $维Bakry-émery曲率分别从下面定界。然后，对于上述一般热方程，我们获得了Li-Yau型梯度估计。我们的研究结果概括了黄马（[4]）和Y.?Li（[6]）的工作。

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《Archivum Mathematicum》 |2016年第4期|共13页
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Nguyen Ngoc Khanh;
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1. Yau type gradient estimates for Delta u plus au(log u)(p) + bu=0 on Riemannian manifolds [J] . Peng Bo, Wang Youde, Wei Guodong Journal of Mathematical Analysis and Applications . 2021,第1期

机译：riemannian歧管上的Delta u plus au（logu）（p）+ bu = 0的Yau型渐变估计
2. Gradient estimates of Hamilton-Souplet-Zhang type for a general heat equation on Riemannian manifolds [J] . Nguyen Thac Dung, Nguyen Ngoc Khanh Archiv der Mathematik . 2015,第5期

机译：黎曼流形上一般热方程的Hamilton-Souplet-Zhang型梯度估计
3. Gradient estimates and Harnack inequalities for Yamabe-type parabolic equations on Riemannian manifolds [J] . Ha Tuan Dung Differential geometry and its applications . 2018,第期

机译：riemannian歧管雅甲型抛物线方程的梯度估计和Harnack不等式
4. Smolyanov surface measures and solutions of Schroedinger and heat type equations on a Riemannian manifold [C] . Ya. A. Butko International Confernce on Days on Diffraction . 2006

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5. Heat equations on Lie groups, symmetric spaces and Riemannian manifolds. [D] . Kim, Jinman. 2005

机译：李群，对称空间和黎曼流形上的热方程。
6. Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation [O] . Bingqing Ma, Yongli Dong -1

机译：加权非线性椭圆方程的梯度估计和Liouville型定理
7. Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds [O] . Khanh, Nguyen Ngoc 2016

机译：黎曼流形上一般热方程的Li Yau型梯度估计。
8. The Conservation Property of the Heat Equation on Riemannian Manifolds [R] . Matthew P. Gaffney 1958

机译：黎曼流形上热方程的守恒性

Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds

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