具有不连续源的弱非线性奇摄动边值问题

J4 ›› 2012, Vol. 47 ›› Issue (2): 8-13.

具有不连续源的弱非线性奇摄动边值问题

丁海云^1,2,倪明康^1,3

1. 华东师范大学数学系, 上海 200062;
2. 上海海事大学数学系, 上海 200135;
3. 上海高校计算科学E研究院上海交通大学研究所, 上海 200240

收稿日期:2011-01-18 出版日期:2012-02-20 发布日期:2012-12-24
作者简介:丁海云（1977- ）,博士研究生，讲师，研究方向为奇摄动理论和方法.Email: hyding@shmtu.edu.cn
基金资助:
上海国家科学基金会资助项目(10ZR1409200); 上海市教育委员会E研究院建设项目（E03004）；上海市重点学科建设项目（B407）

Weak nonlinear singular perturbed boundary value problems with discontinous source terms

DING Hai-yun^1,2, NI Ming-kang^1,3

1. Department of Mathematics, East China Normal University, Shanghai 200062, China;
2. Department of Mathematics, Shanghai Maritime University, Shanghai 200135, China;
3. Division of Computational Science, Einstitute of Shanghai Universities,
Shanghai Jiaotong University, Shanghai 200240, China

Received:2011-01-18 Online:2012-02-20 Published:2012-12-24

摘要/Abstract

摘要：

用边界层函数法讨论了具有不连续源的弱非线性奇摄动边值问题,分区间构造了它的形式渐近解,并通过缝接法对轨道进行连续缝接,在整个区间上证明了解的存在惟一性和渐近解的一致有效性,最后用数值计算验证了结论。

关键词: 奇摄动; 渐近级数; 边界层函数法; 微分流形

Abstract:

A class of weak nonlinear singularly perturbed boundary value problems with discontinuous source terms is examined. Using the method of boundary functions and smooth sewing orbit, the asymptotic solution of this problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is proved. A numerical result illustrats to the theoretical result.

Key words: singular perturbation; asymptotic expansion; boundary layer function; invariable manifold

丁海云1,2,倪明康1,3. 具有不连续源的弱非线性奇摄动边值问题[J]. J4, 2012, 47(2): 8-13.

DING Hai-yun1,2, NI Ming-kang1,3. Weak nonlinear singular perturbed boundary value problems with discontinous source terms[J]. J4, 2012, 47(2): 8-13.

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