A family of singular limits of reaction-diffusion systems of activator-inhibitor type in which stable stationary sharp-interface patterns may form is investigated. For concreteness, the analysis is performed for the FitzHugh-Nagumo model on a suitably rescaled bounded domain in R , with N ≥ 2. It is proved that when the system is sufficiently close to the limit the dynamics starting from the appropriate smooth initial data breaks down into five distinct stages on well-separated time scales, each of which can be approximated by a suitable reduced problem. The analysis allows to follow fully the progressive refinement of spatiotemporal patterns forming in the systems under consideration and provides a framework for understanding the pattern formation scenarios in a large class of physical, chemical, and biological systems modeled by the considered class of reaction-diffusion equations. ∗CMI Université d’Aix-Marseille, 39 rue Frédéric Joliot-Curie 13453 Marseille cedex 13, France †Laboratoire de Mathématiques, CNRS and University Paris-Sud Paris-Saclay, 91405 Orsay Cedex, France ‡Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA

中文翻译：

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活化剂-抑制剂型反应扩散系统中的多尺度模式形成级联

研究了一系列活化剂-抑制剂型反应扩散系统的奇异极限，其中可能形成稳定的固定锐界面图案。为具体起见，在 R 中适当重新缩放的有界域上对 FitzHugh-Nagumo 模型进行分析，其中 N ≥ 2。证明当系统足够接近极限时，从适当的平滑初始数据开始的动力学中断在良好分离的时间尺度上分为五个不同的阶段，每个阶段都可以通过一个合适的简化问题来近似。该分析允许完全遵循所考虑系统中形成的时空模式的逐步细化，并为理解一大类物理、化学、和由所考虑的反应扩散方程类建模的生物系统。∗CMI Université d'Aix-Marseille, 39 rue Frédéric Joliot-Curie 13453 Marseille cedex 13, France †Laboratoire de Mathématiques, CNRS and University Paris-Sud Paris-Saclay, 91405 Orsay Cedex, France ‡Mathetical Sciences, France of New Jersey技术学院，纽瓦克，新泽西州 07102，美国