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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 2
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Original Articles

Gradient estimates for a simple nonlinear heat equation on manifolds

Pages 225-230 | Received 27 Sep 2015, Accepted 07 Nov 2015, Published online: 20 Dec 2015
 

Abstract

In this paper, we study the gradient estimate for positive solutions to the following nonlinear heat equation problem

on the compact Riemannian manifold (Mg) 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.

AMS Subject Classifications:

Notes

The author(s) declare(s) that there isno conflict of interests regarding the publication of this article.

Additional information

Funding

The research is partially supported by the National Natural Science Foundation of China [grant number 11271111].

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