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- Title
GRADIENT ESTIMATES OF LI YAU TYPE FOR A GENERAL HEAT EQUATION ON RIEMANNIAN MANIFOLDS.
- Authors
NGUYEN NGOC KHANH
- Abstract
In th is paper, we consider gradient estimates on complete noncompact Riemannian manifolds (M , g) for the following general heat equation ut = Δ v u + au log u + bu where a is a constant and b is a differentiable function defined on M x [0, ∞). 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.
- Subjects
HEAT equation; RIEMANNIAN manifolds; DIFFERENTIABLE functions; MATHEMATICAL bounds; MATHEMATICS theorems
- Publication
Archivum Mathematicum, 2016, Vol 52, Issue 4, p207
- ISSN
0044-8753
- Publication type
Article
- DOI
10.5817/AM2016-4-207