A generalized Degn–Harrison reaction–diffusion system: Asymptotic stability and non-existence results. (February 2021)

• Record Type: Journal Article
• Authors: Abbad, Abir; Abdelmalek, Salem; Bendoukha, Samir; Gambino, Gaetana
• Is Part Of: Nonlinear analysis. Volume 57(2021)
• Publication Date: 2021-02
• Subjects: Generalized Degn–Harrison system -- Existence of solutions -- Steady states -- Asymptotic stability -- Non-constant steady state solutions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103191
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we study the Degn–Harrison system with a generalized reaction term. Once proved the global existence and boundedness of a unique solution, we address the asymptotic behavior of the system. The conditions for the global asymptotic stability of the steady state solution are derived using the appropriate techniques based on the eigen-analysis, the Poincaré–Bendixson theorem and the direct Lyapunov method. Numerical simulations are also shown to corroborate the asymptotic stability predictions. Moreover, we determine the constraints on the size of the reactor and the diffusion coefficient such that the system does not admit non-constant positive steady state solutions.