Global sharp gradient estimates for a nonlinear parabolic equation on Riemannian manifolds

被引：0

作者：

Chuan, Le Huy ^{[1
]}

Dung, Nguyen Thac ^{[1
]}

Manh, Nguyen Tien ^{[1
]}

机构：

[1] VNU Univ Sci, Fac Math Mech & Informat, Hanoi, Vietnam

来源：

ANALYSIS-INTERNATIONAL MATHEMATICAL JOURNAL OF ANALYSIS AND ITS APPLICATIONS | 2024年 / 44卷 / 03期

关键词：

Bochner techniques; maximum principle; nonlinear parabolic equations; sharp gradient estimates; HEAT-EQUATION;

D O I：

10.1515/anly-2023-0022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we employ the techniques in [C. Cavaterra, S. Dipierro, Z. Gao and E. Valdinoci, Global gradient estimates for a general type of nonlinear parabolic equations, J. Geom. Anal. 32 (2022), no. 2, Paper No. 65] and the approach in [H. T. Dung and N. T. Dung, Sharp gradient estimates for a heat equation in Riemannian manifolds, Proc. Amer. Math. Soc. 147 (2019), no. 12, 5329-5338] to derive sharp gradient estimates for a positive solution to the heat equation u(t) = Delta u + au log uin a complete noncompact Riemannian manifold (where a is a real constant). This is an extension of the gradient estimates of Dung and Dung.

引用

页码：179 / 190

页数：12

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