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http://dx.doi.org/10.4134/BKMS.2013.50.5.1587

HARNACK INEQUALITY FOR A NONLINEAR PARABOLIC EQUATION UNDER GEOMETRIC FLOW

Zhao, Liang (Department of Mathematics Nanjing University of Aeronautics and Astronautics)

Publication Information

Bulletin of the Korean Mathematical Society / v.50, no.5, 2013 , pp. 1587-1598 More about this Journal

Abstract

In this paper, we obtain some gradient estimates for positive solutions to the following nonlinear parabolic equation $\frac{{\partial}u}{{\partial}t}={\triangle}u-b(x,t)u^{\sigma}$ under general geometric flow on complete noncompact manifolds, 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. As an application, we get an interesting Harnack inequality.

Keywords

parabolic equation; positive solutions; geometric flow; Harnack inequality;

Citations & Related Records

Reference

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