Aronson-Benilan estimates for weighted porous medium equations under the geometric flow

被引：0

作者：

Azami, Shahroud ^{[1
]}

机构：

[1] Imam Khomeini Int Univ, Fac Sci, Dept Pure Math, Qazvin, Iran

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 08期

关键词：

geometric flow; gradient estimate; Harnack inequality; porous medium equation; DIFFUSION-EQUATIONS; HEAT-EQUATIONS; RICCI; INEQUALITIES;

D O I：

10.1002/mma.9032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study Aronson-B & eacute;nilan gradient estimates for positive solutions of weighted porous medium equations eth (t)u(x, t) = delta(Phi)u(p)(x, t), (x, t) is an element of M x [0, T]coupled with the geometric flow eth g/ eth t= 2h(t), eth g/ eth t = delta Phi on a complete measure space (Mn, g, e(-Phi)dv). As an application, by integrating the gradient estimates, we derive the corresponding Harnack inequalities.

引用

页码：8988 / 9005

页数：18

共 34 条

[1]

[Anonymous], 1994, Lectures on differential geometry

[2]

Aronson G., 1979, C R ACAD SCI PARIS S, V288, pA103

[3] Gradient estimates for the heat equation under the Ricci flow [J].