A geometrically invariant concept of fast–slow vector fields perturbed by transport terms describing molecular diffusion is proposed in this paper. It is an extension of our concept of singularly perturbed vector fields for ODEs to reaction–diffusion systems with chemical reactions having wide range of characteristic time scales, while transport processes remain comparatively slow. Under this assumption we developed a decomposition into a fast and slow subsystems. It is assumed that the transport terms for the fast subsystem can be neglected to the leading order. For the slow subsystem we modify a concept of singularly perturbed profiles proposed in our previous works. The results are used to justify and to modify an algorithm of reaction–diffusion manifolds (REDIMs). The modified REDIM method is applied to the Michaelis–Menten model to illustrate the suggested approach.

中文翻译：

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反应扩散系统的快慢矢量场

本文提出了由传递术语描述分子扩散的扰动的快慢矢量场的几何不变性概念。这是我们将ODE的奇摄动矢量场概念扩展到化学反应具有特征时间范围广泛的反应扩散系统的过程，而传输过程仍然相对较慢。在这种假设下，我们将分解分解为快速子系统和慢速子系统。假设可以将快速子系统的运输条款忽略为领先顺序。对于慢速子系统，我们修改了我们先前工作中提出的奇摄动轮廓的概念。结果用于证明和修改反应扩散流形（REDIM）的算法。