Some gradient estimates for a diffusion equation on Riemannian manifolds

Abstract

In this note we present some gradient estimates for the diffusion equation ${\partial }_{t}u=\Delta u-\nabla \varphi \cdot \nabla u$ on Riemannian manifolds, where $\varphi$ is a C^2 function, which generalize estimates of R. Hamilton's and Qi S. Zhang's on the heat equation.

3 pages