Gradient estimates for porous medium equations under the Ricci flow

被引：0

作者：

SHEN Li-ju ^{[1
]}

YAO Sha ^{[1
]}

ZHANG Guang-ying ^{[1
]}

REN Xin-an ^{[1
]}

机构：

[1] Department of Mathematics, China University of Mining and Technology

来源：

Applied Mathematics:A Journal of Chinese Universities | 2016年 / 31卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Gradient estimate; porous medium equations; Ricci flow;

D O I：

暂无

中图分类号：

O186.12 [黎曼几何];

学科分类号：

070104 ;

摘要：

A local gradient estimate for positive solutions of porous medium equations on complete noncompact Riemannian manifolds under the Ricci flow is derived. Moreover, a global gradient estimate for such equations on compact Riemannian manifolds is also obtained.

引用

页码：481 / 490

页数：10

共 8 条

[1] Aronson–Bénilan estimates for the porous medium equation under the Ricci flow[J] . Huai-Dong Cao,Meng Zhu.Journal de mathématiques pures et appliquées . 2015 (4)
[2] Gradient estimates of porous medium equations under the Ricci flow
Ma B.
Li J.
[J]. Journal of Geometry, 2014, 105 (2) : 313 - 325
[3] Gradient Estimates for the Porous Medium Equations on Riemannian Manifolds
Huang, Guangyue
Huang, Zhijie
Li, Haizhong
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2013, 23 (04) : 1851 - 1875
[4] Hamilton’s gradient estimates and Liouville theorems for porous medium equations on noncompact Riemannian manifolds[J] . Xiaobao Zhu.Journal of Mathematical Analysis and Applications . 2013
[5] Differential Harnack inequalities on Riemannian manifolds I: Linear heat equation[J] . Junfang Li,Xiangjin Xu.Advances in Mathematics . 2010 (5)
[6] Gradient estimates for the heat equation under the Ricci flow[J] . Mihai Bailesteanu,Xiaodong Cao,Artem Pulemotov.Journal of Functional Analysis . 2009 (10)
[7] Local Aronson–Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds[J] . Peng Lu,Lei Ni,Juan-Luis Vázquez,Cédric Villani.Journal de mathématiques pures et appliquées . 2008 (1)
[8] On the parabolic kernel of the Schr?dinger operator[J] . Peter Li,Shing Tung Yau.Acta Mathematica . 1986 (1)

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