华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (3): 140-148.

• 应用数学与基础数学 • 上一篇    下一篇

奇异奇摄动系统的几何方法

陆海波, 倪明康, 武利猛   

  1. 华东师范大学~~数学系, 上海 200241
  • 收稿日期:2012-06-01 修回日期:2012-09-01 出版日期:2013-05-25 发布日期:2013-07-10

Geometric singular perturbation approach to singular singularly perturbed systems

LU Hai-bo, NI Ming-kang, WU Li-meng   

  1. Department of Mathematics, East China Normal University, Shanghai 200241, China
  • Received:2012-06-01 Revised:2012-09-01 Online:2013-05-25 Published:2013-07-10

摘要: 研究了一类奇异奇摄动系统边值问题.
通过几何奇摄动理论构造了系统的奇异轨道,
并用交换引理证明了解的存在性. 最后用该方法研究了一个经典半导体模型.

关键词: 几何奇摄动, 奇异奇摄动, 交换引理

Abstract: Singularly perturbed systems for which the reduced system
has a manifold of solutions are called singular singularly
perturbed. Boundary value problems for such systems were examined by
geometric singular perturbation approach in this paper. Assumptions
were derived which ensure the existence of a locally unique solution
which is near a singular orbit of the dynamics of limiting fast and
slow systems.

Key words: geometric singular perturbation, singular singularly perturbed, exchange lemma

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