华东师范大学学报(自然科学版) ›› 2006, Vol. 2006 ›› Issue (1): 1-12.

• 奇摄动研究专题：特约综述 •    下一篇

奇摄动问题中的空间对照结构

倪明康1,2   

  1. 1. 华东师范大学 数学系, 上海 200062; 2.上海高校计算科学 E-研究院 上海交通大学研究所, 上海 200030
  • 收稿日期:2005-09-17 修回日期:2005-10-28 出版日期:2006-01-25 发布日期:2006-01-25
  • 通讯作者: 倪明康

Studies in Contrast Spatial Structure Solutions for Singular Perturbation Problems(Chinese)

NI Ming-kang1,2   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062, China; 2. SJTU Section, Computational Science Division, E-Institute of Shanghai Universities, Shanghai 200030, China
  • Received:2005-09-17 Revised:2005-10-28 Online:2006-01-25 Published:2006-01-25
  • Contact: NI Ming-kang

摘要：

综述了从20世纪90年代初开始兴起的对奇摄动问题中空间对照结构解的研究状况.具体介绍了常微分方程中具有阶梯状和脉冲状空间对照结构的一系列工作,其中包括临界情况和非临界情况;同时介绍了变分问题中空间对照结构研究的最新进展,并对偏微分方程中空间对照结构的发展进行了概述.

关键词: 奇摄动, 空间对照结构, 阶梯状结构, 脉冲状结构, 奇摄动, 空间对照结构, 阶梯状结构, 脉冲状结构

Abstract: This paper surveys recent developments in studies of contrast spatial structure solutions of singularly perturbed problems, which have rise since the beginning of 1990's. It mainly introduces a series of work about step-type and spike-type solutions in ODE, including critical and uncritical cases. In the
meanwhile, it introduces the latest research progress of contrast spatial structure of variation problems. The outline of contrast spatial structure solutions in PDE is also included.

Key words: Contrast Spatial Structure Solutions, step-type solutions, spike-type solutions, Singular Perturbation, Contrast Spatial Structure Solutions, step-type solutions, spike-type solutions

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