HARNACK INEQUALITY FOR A NONLINEAR PARABOLIC EQUATION UNDER GEOMETRIC FLOW

Title & Authors
HARNACK INEQUALITY FOR A NONLINEAR PARABOLIC EQUATION UNDER GEOMETRIC FLOW
Zhao, Liang;

Abstract
In this paper, we obtain some gradient estimates for positive solutions to the following nonlinear parabolic equation $\small{\frac{{\partial}u}{{\partial}t}={\triangle}u-b(x,t)u^{\sigma}}$ under general geometric flow on complete noncompact manifolds, where 0 < $\small{{\sigma}}$ < 1 is a real constant and $\small{b(x,t)}$ is a function which is $\small{C^2}$ in the $\small{x}$-variable and $\small{C^1}$ in the$\small{t}$-variable. As an application, we get an interesting Harnack inequality.
Keywords
parabolic equation;positive solutions;geometric flow;Harnack inequality;
Language
English
Cited by
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