右端不连续奇异摄动问题的空间对照结构

doi:10.12066/j.issn.1007-2861.2259

摘要/Abstract

摘要：

主要研究了右端不连续奇异摄动系统中空间对照结构研究状况.介绍了右端不连续的二阶非线性奇异摄动问题的空间对照结构的一系列工作,其中包括半线性系统、拟线性系统和弱非线性系统的Dirichlet问题.同时, 介绍了右端不连续的一阶常微分方程组的齐次Neumann边值问题、一类分段光滑二阶Tikhonov系统Dirichlet边值问题和具有不连续项的奇异摄动抛物方程边值问题.

关键词: 奇异摄动系统, 右端不连续, 空间对照结构, 快慢系统, 边界层函数法, 缝接法

Abstract:

This paper surveys recent developments in spatial contrast structure solutions to singularly perturbed problems with discontinuous right-hand sides. Studies on second-order non-linear singularly perturbed problems, including semi-linear, quasi-linear, and weakly non-linear system Dirichlet problems, are reviewed. In addition, the first-order ordinary differential equations under homogeneous Neumann conditions are discussed. A type of piecewise-continuous second-order Dirichlet problems of the Tikhonov system and boundary value problem of a singularly perturbed parabolic equation with a discontinuous term is also included.

Key words: singularly perturbed system, right end discontinuities, contrast spatial structure solution, slow-fast system, boundary layer function method, sewing connection method

中图分类号:

O175.14

倪明康, 潘亚飞, 吴潇. 右端不连续奇异摄动问题的空间对照结构[J]. 上海大学学报(自然科学版), 2020, 26(6): 853-883.

NI Mingkang, PAN Yafei, WU Xiao. Spatial contrast structure for singular perturbation problems with right end discontinuities[J]. Journal of Shanghai University（Natural Science Edition）, 2020, 26(6): 853-883.

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