| 一类非线性奇摄动Dirichlet边值问题的匹配解法 |
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| 引用本文： | 吴超,欧阳成.一类非线性奇摄动Dirichlet边值问题的匹配解法[J].数学学习,2010,13(4):29-32. |
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| 作者姓名： | 吴超 欧阳成 |
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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： | Y606268)，浙江省新世纪教改项目，湖州师范学院重点教改项目(GJB09004 |
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| 摘 要： | 利用匹配渐近展开法,讨论一类形如εy″+(xn-k)(y′+ym)=0的非线性奇摄动方程的Dirichlet边值问题,并且通过对参数k的五种不同取值的分类探讨,得到了该问题必有左边界层、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类型).进而给出该问题解的零次渐近展开式,推广并改进了已有的结果.
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| 关 键 词： | 非线性 奇摄动 边界层 匹配 渐近展开式 |
The Matching Method for a Class of Dirichlet Boundary Value Problems of Nonlinear Singular Perturbation |
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| WU Chao,OUYANG Cheng.The Matching Method for a Class of Dirichlet Boundary Value Problems of Nonlinear Singular Perturbation[J].Studies In College Mathematics,2010,13(4):29-32. |
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| Authors: | WU Chao OUYANG Cheng |
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| Institution: | (Department of Mathematics, Huzhou Teachers College, Huzhou,313000, PRC) |
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| Abstract: | A class of Dirichlet boundary value problems of nonlinear singularly perturbed equation,εy″＋（x″-k）（y′-y″）=0, is discussed with the matching asymptotic expanding method. According to the five different value of the parameter, It can be drawn out that, the problem must have one of the boundary layer at left, right or interior （either the left or the right boundary layer has two different types）. The zero order asymptotic expansions of the problems are also given, and the result known is improved and generalized. |
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| Keywords: | Nonlinear singular perturbation boundary layer matching asymptotic expansion |
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