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

被引：0
|
作者：
Abolarinwa, Abimbola [1 ]
Osilagun, Johnson A. [1 ]
Azami, Shahroud [2 ]
机构：
[1] Univ Lagos, Fac Sci, Dept Math, Lagos, Nigeria
[2] Imam Khomeini Int Univ, Dept Pure Math, Fac Sci, Qazvin, Iran
来源：
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2024年 / 21卷 / 06期
关键词：
Riemannian manifolds; gradient estimates; Harnack inequalities; Ricci curvature; reaction-diffusion equation; ALLEN-CAHN EQUATION; DIFFERENTIAL HARNACK; TRAVELING-WAVES; HEAT-EQUATIONS; POTENTIALS; MOTION;
D O I：
10.1142/S0219887824501111
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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.
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页数：18
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