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December, 2020 Gradient Estimates for the Nonlinear Parabolic Equation with Two Exponents on Riemannian Manifolds
Songbo Hou
Taiwanese J. Math. 24(6): 1439-1448 (December, 2020). DOI: 10.11650/tjm/200401

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 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).

Citation

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Songbo Hou. "Gradient Estimates for the Nonlinear Parabolic Equation with Two Exponents on Riemannian Manifolds." Taiwanese J. Math. 24 (6) 1439 - 1448, December, 2020. https://doi.org/10.11650/tjm/200401

Information

Received: 12 February 2019; Revised: 29 March 2020; Accepted: 5 April 2020; Published: December, 2020
First available in Project Euclid: 19 November 2020

MathSciNet: MR4176881
Digital Object Identifier: 10.11650/tjm/200401

Subjects:
Primary: 35K55, 58J35

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

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Vol.24 • No. 6 • December, 2020
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