一类拟线性奇异摄动方程组的空间对照结构  

The Contrast Structure for the Quasi-Linear Singularly Perturbed Equations

作　　者：陈华雄 左俊梅 倪明康[2] CHEN Huaxiong;ZUO Junmei;NI Mingkang(School of mathematics and statistics, Zhoukou Normal University, China;Department of Mathematics, East China Normal University, China） Zhoukou 466000, Shanghai 200241, China)

机构地区：[1]周口师范学院数学与统计学院,河南周口466000 [2]华东师范大学数学系,上海200241

出　　处：《应用数学》2018年第3期668-673,共6页Mathematica Applicata

基　　金：国家自然科学基金(61703447);河南省科技攻关项目(162102310604;172102310123);周口师范学院科研基金项目(ZKNUC2016012;ZKNUC2017020;ZKNUB2201806);河南省高等学校重点科研项目(18A110039)

摘　　要：本文研究带慢变量的右边不连续的拟线性奇异摄动方程组的空间对照结构.利用边界层函数法构造了该方程组的形式渐近解,并运用"缝接法"证明问题解的存在性以及渐近解的一致有效性.最后,通过例子验证了所得结果的有效性.This paper discusses the contrast structure solution for the quasi-linear singularly perturbed equations with slow variable and discontinuous righthand side. By applying the boundary layer function method, the asymptotic solution of this problem is constructed. Then using the sewing connection method, the existence of the solution is shown and the asymptotic solution is proved to be uniformly valid. Finally, an example is given to illustrate the main results.

关 键 词：奇异摄动 空间对照结构 边界层函数法 缝接法 

分 类 号：O29[理学—应用数学]