Gradient estimates for a simple nonlinear heat equation on manifolds. Issue 2 (25th January 2017)

• Record Type: Journal Article
• Authors: Ma, Li
• Is Part Of: Applicable analysis. Volume 96:Issue 2(2017)
• Page Start: 225
• Page End: 230
• Publication Date: 2017-01-25
• Subjects: Positive solution -- nonlinear heat equation -- gradient estimate; 53C21 -- 35J60; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1120290
• Languages: English
• ISSNs: 0003-6811

Abstract

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.