Taiwanese Journal of Mathematics

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

Songbo Hou

Advance publication

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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 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).

Article information

Source
Taiwanese J. Math., Advance publication (2020), 10 pages.

Dates
First available in Project Euclid: 14 April 2020

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1586851304

Digital Object Identifier
doi:10.11650/tjm/200401

Subjects
Primary: 35K55: Nonlinear parabolic equations 58J35: Heat and other parabolic equation methods

Keywords
gradient estimate nonlinear parabolic equation Liouville theorem

Citation

Hou, Songbo. Gradient Estimates for the Nonlinear Parabolic Equation with Two Exponents on Riemannian Manifolds. Taiwanese J. Math., advance publication, 14 April 2020. doi:10.11650/tjm/200401. https://projecteuclid.org/euclid.twjm/1586851304


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