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arXiv · 2101.05115

Gradient estimates for the nonlinear parabolic equation with two exponents on Riemannian manifolds

Songbo Hou
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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).

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Songbo Hou. 2021-01-13. Gradient estimates for the nonlinear parabolic equation with two exponents on Riemannian manifolds. https://arxiv.org/abs/2101.05115

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