Gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces

被引：10
|
作者：
Yang, Fei [1 ]
Zhang, Liangdi [2 ]
机构：
[1] China Univ Geosci, Sch Math & Phys, Wuhan 430074, Hubei, Peoples R China
[2] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Zhejiang, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2019年 / 187卷
关键词：
Gradient estimates; Harnack inequality; Nonlinear parabolic equation; Smooth metric measure space; THEOREM; KERNEL;
D O I：
10.1016/j.na.2019.03.017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let (M-n, g, e(-phi dv)) be a smooth metric measure space. In this paper, we derive a series of gradient estimates and a Harnack inequality for positive solutions of a nonlinear parabolic partial differential equation (Delta(phi) - partial derivative(t))u = qu + au(ln u)(alpha) in M-n x (-infinity,+infinity), where q is an element of C-2,C-1 (M-n x (-infinity,+infinity)) and a, a is an element of R. (C) 2019 Elsevier Ltd. All rights reserved.
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页码：49 / 70
页数：22
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