Abstract
In this paper, we study the gradient estimate for positive solutions to the following nonlinear heat equation problem
on the compact Riemannian manifold (M, g) of dimension n and with non-negative Ricci curvature. Here is a constant, V is a smooth function on M with for some positive constant A. This heat equation is a basic evolution equation and it can be considered as the negative gradient heat flow to W-functional (introduced by G.Perelman), which is the Log-Sobolev inequalities on the Riemannian manifold and V corresponds to the scalar curvature.
Notes
The author(s) declare(s) that there isno conflict of interests regarding the publication of this article.