Stability of traveling wave fronts for delayed Belousov–Zhabotinskii models with spatial diffusion. Issue 6 (25th April 2020)

• Record Type: Journal Article
• Authors: Meng, Yanling; Zhang, Weiguo; Yu, Zhixian
• Is Part Of: Applicable analysis. Volume 99:Issue 6(2020)
• Page Start: 922
• Page End: 941
• Publication Date: 2020-04-25
• Subjects: Ming Mei; Stability -- Belousov–Zhabotinskii model -- comparison principle -- weighted energy method -- traveling wave fronts; 35C07 -- 92D25 -- 35B35; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1514113
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: This paper is concerned with the stability of traveling wave fronts of a delayed Belousov–Zhabotinskii model with spatial diffusion. The existence and comparison theorem of solutions of the corresponding Cauchy problem in a weight space are established for the system on R by appealing to the theories of semigroup and abstract functional differential equations. By means of comparison principle and the weighted energy method, we prove that the traveling wave solutions are exponentially stable, when the initial perturbation around the traveling waves decays exponentially as x → − ∞, but in other locations, the initial data can be arbitrarily large.