| 一类非线性奇摄动边值问题的渐近解 |
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| 引用本文： | 方旭旭,欧阳成,韩祥临.一类非线性奇摄动边值问题的渐近解[J].安徽师范大学学报(自然科学版),2012,35(1):16-20. |
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| 作者姓名： | 方旭旭 欧阳成 韩祥临 |
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| 作者单位： | 湖州师范学院数学系,浙江湖州,313000 |
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| 基金项目： | 国家自然科学基金项目(11071205,10902076);浙江省自然科学基金项目(Y6110502);浙江省精品课程《常微分方程》 |
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| 摘 要： | 利用匹配渐近展开法,研究了一类带参数的非线性奇摄动边值问题.首先找到满足退化方程的外部解,然后根据参数k的变化分五种情况找到用特殊函数表示的内层解,得到了该问题具有左边界层、右边界层或内部层之一的结论(其中左、右边界层又各分为两种情况).最后通过匹配原则,将内外展开式进行匹配给出了该问题的一致有效的零阶渐近展开式.
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| 关 键 词： | 非线性 奇摄动 边界层 匹配 渐近解 |
Asymptotic Solutions for a Class of Nonlinear Singularly Perturbed Boundary Value Problems |
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| FANG Xu-xu
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OU Yang-cheng
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HAN Xiang-lin.Asymptotic Solutions for a Class of Nonlinear Singularly Perturbed Boundary Value Problems[J].Journal of Anhui Normal University(Natural Science Edition),2012,35(1):16-20. |
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| Authors: | FANG Xu-xu OU Yang-cheng HAN Xiang-lin |
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| Institution: | (Department of Mathematics,Huzhou Teachers College,Huzhou 313000,China) |
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| Abstract: | A class of nonlinear singularly perturbed problems with parameter is discussed using the matching asymptotic expanding method.Firstly,the outer solutions to satisfy the degenerate equation are found.The inner solutions expressed with special function are gotten as the five different cases of parameter,then the conclusion that the problem must have one of the boundary layers at left,right and interior(where the left boundary layer has two different cases and also the right) is obtained.Finally,zero-order uniformly valid asymptotic expansions of the problem are given by matching the outer and inner solutions according to the matching principle. |
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| Keywords: | nonlinear singular perturbation boundary layer matching asymptotic solution |
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