| 一类边界层位置转移的非线性奇摄动问题 |
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| 引用本文： | 吴超,欧阳成.一类边界层位置转移的非线性奇摄动问题[J].大学数学,2012(1):41-44. |
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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 |
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| 基金项目： | 国家自然科学基金(11071205);浙江省自然科学基金(Y6110502);浙江省新世纪教改项目(ZC09063);浙江省精品课程《常微分方程》项目 |
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| 摘 要： | 利用匹配渐近展开法,讨论了一类边界层位置转移的非线性奇摄动边值问题,并且通过对参数的五种不同取值的分类探讨,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类型).进而给出了该问题解的一致有效的零次渐近解,推广并改进了已有的结果.
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| 关 键 词： | 非线性奇摄动方程 边界层 匹配 特异极限 渐近展开式 |
A Class of Nonlinear Singularly Perturbed Problems with Changed Position of Boundary Layer |
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| WU Chao,OUYANG Cheng.A Class of Nonlinear Singularly Perturbed Problems with Changed Position of Boundary Layer[J].College Mathematics,2012(1):41-44. |
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| Authors: | WU Chao OUYANG Cheng |
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| Institution: | (Department of Mathematics,Huzhou Teachers College,Huzhou 313000,China) |
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| Abstract: | A class of boundary value problems of nonlinear singular perturbation is discussed using the matching asymptotic expanding method.The conclusions that the problem must have one of the boundary layer at left,right and interior(where the left boundary layer has two different types and also the right) are obtained through the classified discussion of the five different value of parameter.Then,the zero order asymptotic solutions of the problems are given,and the result that has been known is improved and generalized. |
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| Keywords: | nonlinear singular perturbation boundary layer matching special limit asymptotic expansion |
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