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- Title
A Harnack inequality for a class of 1D nonlinear reaction–diffusion equations and applications to wave solutions.
- Authors
Abolarinwa, Abimbola; Osilagun, Johnson A; Azami, Shahroud
- 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.
- Subjects
REACTION-diffusion equations; NONLINEAR equations; WAVE equation; RIEMANNIAN manifolds; PLANE geometry
- Publication
International Journal of Geometric Methods in Modern Physics, 2024, Vol 21, Issue 6, p1
- ISSN
0219-8878
- Publication type
Article
- DOI
10.1142/S0219887824501111