This paper considers a Belousov–Zhabotinskii reaction–diffusion system with spatio-temporal delay. The spatio-temporal delay is modeled as the convolution of with a kernel function , where . By constructing an auxiliary system, applying Schauder’s fixed point theorem, and using a limiting argument, we demonstrate that the model admits non-negative traveling wave solutions connecting the equilibrium to some unknown positive steady states (also referred to as a semi-wavefront) when the wave speed satisfies . Moreover, no such semi-wavefront exists if . It is noteworthy that the kernel function is not required to have compact support in this analysis.

中文翻译：

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具有时空延迟的 Belousov–Zhabotinskii 反应扩散系统的半波前


本文考虑具有时空延迟的 Belousov-Zhabotinskii 反应扩散系统。时空延迟被建模为 与核函数 的卷积，其中 。通过构建辅助系统，应用 Schauder 不动点定理，并使用极限参数，我们证明该模型允许非负行波解，将平衡连接到一些未知的正稳态（也称为半波前）：波速满足 .此外，如果 ，则不存在这样的半波前。值得注意的是，在此分析中不需要核函数具有紧凑的支持。