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| Gradient Estimates for a Nonlinear Diffusion Equation on Complete Manifolds |
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Citation： |
Jiaxian WU,Qihua RUAN,Yihu YANG.Gradient Estimates for a Nonlinear Diffusion Equation on Complete Manifolds[J].Chinese Annals of Mathematics B,2015,36(6):1011~1018 |
| Page view： 1193
Net amount： 916 |
Authors： |
Jiaxian WU; Qihua RUAN;Yihu YANG |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.\,11171253, 11471175), the Fujian
Provincial National Natural Science Foundation of China
(No.\,2012J01015) and the Startup Foundation for Introducing Talent
of Nuist(No.\,2014r030) and the Pre-research Foundation of
NSFC(No.\,2014x025). |
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| Abstract： |
This paper deals with the gradient estimates of the Hamilton type
for the positive solutions to the following nonlinear diffusion
equation:
\begin{align}
u_t=\triangle u + \nabla\phi \cdot \nabla u + a(x)u\ln u + b(x)u
\nonumber
\end{align}
on a complete noncompact Riemannian manifold with a Bakry-Emery {\rm
Ric}ci curvature bounded below by $-K$ ($K \ge 0$), where $\phi$ is
a $C^2$ function, $a(x)$ and $b(x)$ are $C^1$ functions with certain
conditions. |
Keywords： |
Gradient estimate, Bakry-Emery Ricci curvature, Nonlinear diffusion
equation |
Classification： |
58J35 |
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