Geodesic
Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds
Archivum mathematicum, Tome 52 (2016) no. 4, pp. 207-219

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In this paper, we consider gradient estimates on complete noncompact Riemannian manifolds $(M,g)$ for the following general heat equation \[ u_t=\Delta _V u+au\log u+bu \] where $a$ is a constant and $b$ is a differentiable function defined on $M\times [0, \infty )$. 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.
DOI : 10.5817/AM2016-4-207
Classification : 35B53, 58J35
Keywords: gradient estimates; general heat equation; Laplacian comparison theorem; $V$-Bochner-Weitzenböck; Bakry-Emery Ricci curvature 
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     author = {Khanh, Nguyen Ngoc},
     title = {Gradient estimates of {Li} {Yau} type for a general heat equation on {Riemannian} manifolds},
     journal = {Archivum mathematicum},
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Khanh, Nguyen Ngoc. Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds. Archivum mathematicum, Tome 52 (2016) no. 4, pp. 207-219. doi: 10.5817/AM2016-4-207

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