LocalAronson-Benilan Estimates for Porous Medium Equations under Ricci Flow

被引：1
|
作者：
Zhu, Xiaobao [1 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
来源：
JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS | 2011年 / 24卷 / 04期
关键词：
Aronson-Benilan estimate; Porous medium equation; Ricci flow; Harnack inequality;
D O I：
10.4208/jpde.v24.n4.4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work we derive local gradient estimates of the Aronson-Benilan type for positive solutions of porous medium equations under Ricci flow with bounded Ricci curvature. As an application, we derive a Harnack type inequality.
引用
收藏
页码：324 / 333
页数：10
相关论文
共 50 条
  • [21] Spatial decay estimates for flow in a porous medium
    Chadam, J
    Qin, Y
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1997, 28 (04) : 808 - 830
  • [22] Gradient Estimates for the Porous Medium Equations on Riemannian Manifolds
    Huang, Guangyue
    Huang, Zhijie
    Li, Haizhong
    JOURNAL OF GEOMETRIC ANALYSIS, 2013, 23 (04) : 1851 - 1875
  • [23] Decay Estimates for Solutions of Porous Medium Equations with Advection
    Nicolau M. L. Diehl
    Lucineia Fabris
    Juliana S. Ziebell
    Acta Applicandae Mathematicae, 2020, 165 : 149 - 162
  • [24] Gradient Estimates for the Porous Medium Equations on Riemannian Manifolds
    Guangyue Huang
    Zhijie Huang
    Haizhong Li
    Journal of Geometric Analysis, 2013, 23 : 1851 - 1875
  • [25] Decay Estimates for Solutions of Porous Medium Equations with Advection
    Diehl, Nicolau M. L.
    Fabris, Lucineia
    Ziebell, Juliana S.
    ACTA APPLICANDAE MATHEMATICAE, 2020, 165 (01) : 149 - 162
  • [26] GRADIENT ESTIMATES FOR A NONLINEAR PARABOLIC EQUATION UNDER RICCI FLOW
    Hsu, Snu-Yu
    DIFFERENTIAL AND INTEGRAL EQUATIONS, 2011, 24 (7-8) : 645 - 652
  • [27] HARNACK ESTIMATES FOR THE LINEAR HEAT EQUATION UNDER THE RICCI FLOW
    Zhu, Xiaorui
    PACIFIC JOURNAL OF MATHEMATICS, 2011, 252 (01) : 245 - 256
  • [28] GRADIENT ESTIMATES FOR SOLUTIONS OF THE HEAT EQUATION UNDER RICCI FLOW
    Liu, Shiping
    PACIFIC JOURNAL OF MATHEMATICS, 2009, 243 (01) : 165 - 180
  • [29] On Evolution Equations Under the Hamilton’s Ricci Flow
    Vladimir Rovenski
    Sergey Stepanov
    Irina Tsyganok
    Results in Mathematics, 2020, 75
  • [30] Harnack estimates for a nonlinear parabolic equation under Ricci flow
    Li, Yi
    Zhu, Xiaorui
    DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2018, 56 : 67 - 80
12345