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 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 , but in other locations, the initial data can be arbitrarily large.

中文翻译：

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具有空间扩散的延迟 Belousov-Zhabotinskii 模型行波前的稳定性

摘要 本文关注具有空间扩散的延迟 Belousov-Zhabotinskii 模型行波前的稳定性。借助半群理论和抽象泛函微分方程理论，建立了系统上相应柯西问题在权空间中解的存在性和比较定理。通过比较原理和加权能量法，我们证明了行波解是指数稳定的，当行波周围的初始扰动指数衰减为 时，但在其他位置，初始数据可以任意大。