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^*

^*此作品的通讯作者

数学科学学院

University of Macau
Lehigh University

科研成果: 期刊稿件 › 文章 › 同行评审

17 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	729-748
页数	20
期刊	Journal des Mathematiques Pures et Appliquees
卷	104
期	4
DOI	https://doi.org/10.1016/j.matpur.2015.05.001
出版状态	已出版 - 1 10月 2015

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10.1016/j.matpur.2015.05.001

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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",

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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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JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

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ER -

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

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