Stabilization to a positive equilibrium for some reaction–diffusion systems. (December 2021)

• Record Type: Journal Article
• Authors: Guo, Jong-Shenq; Shimojo, Masahiko
• Is Part Of: Nonlinear analysis. Volume 62(2021)
• Publication Date: 2021-12
• Subjects: Stabilization -- Equilibrium -- Reaction–diffusion system -- Entire solution -- Lyapunov functional; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103378
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The aim of this paper is to study the asymptotic behavior of solutions for some reaction–diffusion systems in biology. First, we establish a Liouville type theorem for entire solutions of these reaction–diffusion systems. Based on this theorem, we derive the stabilization of the solutions of the reaction–diffusion system to the unique positive constant state, under the condition that this positive constant state is globally stable in the corresponding kinetic systems. Two specific examples about spreading phenomena from ecology and epidemiology are given to illustrate the application of this theory.