一类非线性奇摄动问题的渐近解  

The Asymptotic Solution of a Class of Nonlinear Singularly Perturbed Problems

作　　者：方静[1] 欧阳成[1] 

机构地区：[1]湖州师范学院数学系,浙江湖州313000

出　　处：《安徽师范大学学报（自然科学版）》2013年第1期21-23,共3页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金(11071205;10902076);浙江省自然科学基金(Y6110502);浙江省精品课程<常微分方程>

摘　　要：利用匹配渐近展开法,研究了一类无限长区域上的非线性奇摄动边值问题,给出了解的一致有效的一阶渐近展开式.先求出外展开式,利用收缩变换求出内展开式.利用广义积分和Taylor展开将内外展开式进行匹配,进而得到一致有效的复合展开式.通过对这类新的无限长区域上非线性问题的研究,拓宽了类似问题的研究范围,为相关奇摄动问题的研究提供了参考.Using the matching asymptotic expansion method, a class of nonlinear singularly perturbed boundary value problems on an infinite long region is studied, and the uniformly valid asymptotic expansion with the first order for the solution is given. First solving the outer expansion, and then solving interior expansion with the contraction transformation. Using the generalized integral and Taylor expansion, the internal expansion and the outer one are matched, and the uniformly valid compound expansion is obtained. Through studying this class of new nonlinear problems on the infinite long region, the studied range of the similar problems is expanded. And it is provided with a reference for the research on the related singularly perturbed problems.

关 键 词：匹配渐近展开法 无限长区域 收缩变换 一致有效 边值 

分 类 号：O175.14[理学—数学]