| 具有不连续源的弱非线性奇摄动边值问题 |
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| 引用本文： | 丁海云,倪明康. 具有不连续源的弱非线性奇摄动边值问题[J]. 山东大学学报(理学版), 2012, 47(2): 8-13 |
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| 作者姓名： | 丁海云 倪明康 |
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| 作者单位： | 1. 华东师范大学数学系,上海200062／上海海事大学数学系,上海200135
2. 华东师范大学数学系,上海200062／上海高校计算科学E-研究院上海交通大学研究所,上海200240 |
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| 基金项目： | 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) |
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| 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。
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| 关 键 词： | 奇摄动 渐近级数 边界层函数法 微分流形 |
| 收稿时间： | 2011-01-18 |
Weak nonlinear singular perturbed boundary value problems with discontinous source terms |
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| DING Hai-yun,NI Ming-kang. Weak nonlinear singular perturbed boundary value problems with discontinous source terms[J]. Journal of Shandong University, 2012, 47(2): 8-13 |
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| Authors: | DING Hai-yun NI Ming-kang |
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| Affiliation: | 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) |
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| 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. |
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| Keywords: | singular perturbation asymptotic expansion boundary layer function invariable manifold |
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