右端不连续奇异摄动问题的空间对照结构  

Spatial contrast structure for singular perturbation problems with right end discontinuities

作　　者：倪明康 潘亚飞 吴潇 NI Mingkang;PAN Yafei;WU Xiao(School of Mathematical Sciences,East China Normal University,Shanghai 200062,China;Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice,Shanghai 200062,China;Department of Mathematics and Physics,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]华东师范大学数学科学学院,上海200062 [2]上海市核心数学与实践重点实验室,上海200062 [3]南京工程学院数理部,南京211167

出　　处：《上海大学学报（自然科学版）》2020年第6期853-883,共31页Journal of Shanghai University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11871217);上海市科委基金资助项目(A18DZ2271000)。

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.This paper surveys recent developments in spatial contrast structure solutions to singularly perturbed problems with discontinuous right-hand sides.Studies on secondorder 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.

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 

分 类 号：O175.14[理学—数学]