Aronson-B\'enilan estimates for the fast diffusion equation under the Ricci flow
Differential Geometry
2016-07-29 v1 Analysis of PDEs
Abstract
We study the fast diffusion equation (FDE) with a linear forcing term under the Ricci flow on complete manifolds with bounded curvature and nonnegative curvature operator. We prove Aronson-B\'enilan and Li-Yau-Hamilton type differential Harnack estimates for positive solutions of the FDE. In addition, we use similar method to prove certain Li-Yau-Hamilton estimates for the heat equation and conjugate heat equation which extend those obtained by X. Cao and R. Hamilton, X. Cao, and S. Kuang and Q. Zhang to noncompact setting.
Keywords
Cite
@article{arxiv.1607.08555,
title = {Aronson-B\'enilan estimates for the fast diffusion equation under the Ricci flow},
author = {Huai-Dong Cao and Meng Zhu},
journal= {arXiv preprint arXiv:1607.08555},
year = {2016}
}