Qualitative properties of pulsating fronts for reaction–advection–diffusion equations in periodic excitable media. (February 2022)

• Record Type: Journal Article
• Authors: Bu, Zhen-Hui; He, Jun-Feng
• Is Part Of: Nonlinear analysis. Volume 63(2022)
• Publication Date: 2022-02
• Subjects: Reaction–advection–diffusion equations -- Periodic excitable media -- Pulsating fronts -- Asymptotic behavior; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103418
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we study the pulsating fronts of reaction–advection-diffusion equations with two types of nonlinear term in periodic excitable media. Firstly, for the case with combustion nonlinearity, the unique front is proved to decay exponentially when it approaches the unstable limiting state. Secondly, for the degenerate monostable type nonlinearity, it is shown that the front with critical speed is unique, monotone and decays exponentially at negative end, while the fronts of noncritical speeds decay to zero non-exponentially.