Gradient Estimates and Harnack Inequality for a Nonlinear Parabolic Equation on Complete Manifolds

被引：2

作者：

Wu J. ^{[1
]}

Yang Y.-H. ^{[2
]}

机构：

[1] Department of Mathematics, Tongji University, Shanghai

[2] Department of Mathematics, Shanghai Jiao Tong University, Shanghai

来源：

Communications in Mathematics and Statistics | 2013年 / 1卷 / 4期

基金：

中国国家自然科学基金;

关键词：

Gradient estimate; Harnack inequality; Nonlinear parabolic equation; Ricci curvature;

D O I：

10.1007/s40304-014-0026-x

中图分类号：

学科分类号：

摘要：

Let M be a noncompact complete Riemannian manifold. In this paper, we consider the following nonlinear parabolic equation on Mut Ut (x, t) = Δu(x, t) + au(x, t) ln u(x, t) + buα(x, t)..We prove a Li–Yau type gradient estimate for positive solutions to the above equation; as an application, we also derive the corresponding Harnack inequality. These results generalize the corresponding ones proved by Li (J Funct Anal 100:233–256, 1991). © 2014, School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag Berlin Heidelberg.

引用

页码：437 / 464

页数：27

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