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| Gradient Estimates for a Nonlinear Parabolic Equationwith Diffusion on Complete Noncompact Manifolds |
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Citation： |
Liang ZHAO,Zongwei MA.Gradient Estimates for a Nonlinear Parabolic Equationwith Diffusion on Complete Noncompact Manifolds[J].Chinese Annals of Mathematics B,2015,36(1):57~66 |
| Page view： 1715
Net amount： 1592 |
Authors： |
Liang ZHAO; Zongwei MA; |
Foundation： |
supported by the Jiangsu Provincial Natural Science Foundation of China (No.
BK20140804) and the Fundamental Research Funds of the Central Universities (No. NS2014076). |
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| Abstract： |
The authors obtain some gradient estimates for positive solutions
to the following nonlinear parabolic
equation:
$$
\frac{\partial u}{\partial t}=\triangle u-b(x, t)u^{\sigma}
$$
on complete noncompact manifolds with Ricci curvature bounded from below, where $0<\sigma<1$ is a
real constant, and $b(x, t)$ is a function which is $C^{2}$ in the $x$-variable and $C^{1}$ in the $t$-variable. |
Keywords： |
Gradient estimates, Positive solutions, Harnack inequality |
Classification： |
58J05, 58J35 |
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