Gradient Estimates for the Nonlinear Parabolic Equation with Two Exponents on Riemannian Manifolds

被引：1

作者：

Hou, Songbo ^{[1
]}

机构：

[1] China Agr Univ, Coll Sci, Dept Appl Math, Beijing 100083, Peoples R China

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2020年 / 24卷 / 06期

关键词：

gradient estimate; nonlinear parabolic equation; Lionville theorem; THEOREM;

D O I：

10.11650/tjm/200401

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the nonlinear parabolic equation with two exponents on complete noncompact Riemannian maniflods. The special types of such equation include the Fisher-KPP equation, the parabolic Allen-Cahn equation and the Newell-Whitehead equation. We get the Souplet-Zhang's gradient estimates for the positive solutions to such equation. We also obtain the Liouville theorem for positive ancient solutions. Our results extend those of Souplet-Zhang (Bull. London. Math. Soc. 38 (2006), 1045-1053) and Zhu (Acta Math. Sci. Ser. B 36 (2016), no. 2, 514-526).

引用

页码：1439 / 1448

页数：10

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