Research ArticleNo Access

A Harnack inequality for a class of $1$ D nonlinear reaction–diffusion equations and applications to wave solutions

Abimbola Abolarinwa

https://orcid.org/0000-0003-3478-4854

Department of Mathematics, Faculty of Science, University of Lagos, Akoka, Lagos, Nigeria

E-mail Address: a.abolarinwa1@gmail.com

E-mail Address: aabolarinwa@unilag.edu.ng

Corresponding author.

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Johnson A Osilagun

Department of Mathematics, Faculty of Science, University of Lagos, Akoka, Lagos, Nigeria

E-mail Address: josilagun@unilag.edu.ng

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, and

Shahroud Azami

https://orcid.org/0000-0002-8976-2014

Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran

E-mail Address: azami@sci.ikiu.ac.ir

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https://doi.org/10.1142/S0219887824501111Cited by:1 (Source: Crossref)

Abstract

In this paper, a differential-geometric method is applied to build some Li–Yau–Hamilton-type Harnack inequalities for the positive solutions to a one spatial dimensional nonlinear reaction–diffusion equation in a plane geometry. The class of reaction–diffusion equation that is considered here contains several important equations some of which are Newel–Whitehead–Segel, Allen–Cahn and Fisher–KPP equations. The Harnack inequalities so derived are used to discuss some other important properties of positive solutions and in the characterization of positive wave solutions.

Keywords:

AMSC: 35B50, 53C44, 58J60, 58J35, 60J60

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