Aronson-Bénilan estimates for the porous medium equation under the Ricci flow

Huai Dong Cao; Meng Zhu

doi:10.1016/j.matpur.2015.05.001

Aronson-Bénilan estimates for the porous medium equation under the Ricci flow

Huai Dong Cao
, Meng Zhu^*

^*Corresponding author for this work

School of Mathematical Sciences

University of Macau
Lehigh University

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

In this paper we study the porous medium equation (PME) coupled with the Ricci flow on complete manifolds with bounded curvature and nonnegative curvature operator. In particular, we derive Aronson-Bénilan and Li-Yau-Hamilton type differential Harnack estimates for positive solutions to the PME under the Ricci flow.

Original language	English
Pages (from-to)	729-748
Number of pages	20
Journal	Journal des Mathematiques Pures et Appliquees
Volume	104
Issue number	4
DOIs	https://doi.org/10.1016/j.matpur.2015.05.001
State	Published - 1 Oct 2015

Keywords

Aronson-Bénilan estimate
Harnack inequality
Porous medium equation
Ricci flow

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10.1016/j.matpur.2015.05.001

Cite this

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title = "Aronson-B{\'e}nilan estimates for the porous medium equation under the Ricci flow",

abstract = "In this paper we study the porous medium equation (PME) coupled with the Ricci flow on complete manifolds with bounded curvature and nonnegative curvature operator. In particular, we derive Aronson-B{\'e}nilan and Li-Yau-Hamilton type differential Harnack estimates for positive solutions to the PME under the Ricci flow.",

keywords = "Aronson-B{\'e}nilan estimate, Harnack inequality, Porous medium equation, Ricci flow",

author = "Cao, \{Huai Dong\} and Meng Zhu",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Masson SAS.",

year = "2015",

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AU - Cao, Huai Dong

AU - Zhu, Meng

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N2 - In this paper we study the porous medium equation (PME) coupled with the Ricci flow on complete manifolds with bounded curvature and nonnegative curvature operator. In particular, we derive Aronson-Bénilan and Li-Yau-Hamilton type differential Harnack estimates for positive solutions to the PME under the Ricci flow.

AB - In this paper we study the porous medium equation (PME) coupled with the Ricci flow on complete manifolds with bounded curvature and nonnegative curvature operator. In particular, we derive Aronson-Bénilan and Li-Yau-Hamilton type differential Harnack estimates for positive solutions to the PME under the Ricci flow.

KW - Aronson-Bénilan estimate

KW - Harnack inequality

KW - Porous medium equation

KW - Ricci flow

UR - https://www.scopus.com/pages/publications/84941184261

U2 - 10.1016/j.matpur.2015.05.001

DO - 10.1016/j.matpur.2015.05.001

M3 - 文章

AN - SCOPUS:84941184261

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VL - 104

SP - 729

EP - 748

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 4

ER -

Aronson-Bénilan estimates for the porous medium equation under the Ricci flow

Abstract

Keywords

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