Gradient estimates for the nonlinear parabolic equation with two exponents on Riemannian manifolds
Differential Geometry
2021-01-14 v1
Abstract
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 gradeint 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. 38:1045-1053, 2006) and Zhu (Acta Mathematica Scientia 36B(2): 514-526, 2016).
Keywords
Cite
@article{arxiv.2101.05115,
title = {Gradient estimates for the nonlinear parabolic equation with two exponents on Riemannian manifolds},
author = {Songbo Hou},
journal= {arXiv preprint arXiv:2101.05115},
year = {2021}
}
Comments
8 pages