| 一类非线性奇摄动问题边界层与边值的关系 |
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| 引用本文： | 周倩,陈松林.一类非线性奇摄动问题边界层与边值的关系[J].合肥学院学报(自然科学版),2011(4):12-15. |
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| 作者姓名： | 周倩 陈松林 |
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| 作者单位： | 安徽工业大学数理学院; |
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| 基金项目： | 国家自然基金项目(41075027D0503); 科技部创新方法专项子项目(2009IM010400)资助 |
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| 摘 要： | 利用匹配渐近展开法,讨论了一类二阶非线性奇摄动问题εy″＋yy＇＋xy＋y^2=0,x∈（0,1）,y（0）=α,y（1）=β,通过匹配方程的内层解、外部解及边界层解,得出解的层性态与边界条件的关系,并给出了解的渐近表示.
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| 关 键 词： | 非线性方程 边界层 内部层 匹配渐近展开 |
The Relation Between Boundary Layer and Boundary-value for A Class of Nonlinear Singularly Perturbed Problem |
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| ZHOU Qian,CHEN Song-lin.The Relation Between Boundary Layer and Boundary-value for A Class of Nonlinear Singularly Perturbed Problem[J].Journal of Hefei University :Natural Sciences,2011(4):12-15. |
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| Authors: | ZHOU Qian CHEN Song-lin |
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| Institution: | ZHOU Qian,CHEN Song-lin(School of Mathe and Physics,Anhui University of Technology,Maanshan,Anhui 243032,China) |
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| Abstract: | The solution for a class of nonlinear singularly perturbed equation of second-order εy″+yy′+xy+y2=0,x∈(0,1),y(0)=α,y(1)=β is considered by using the method of matched asymptotic expansion.The relation between the layer’s quality of its solution and its boundary conditions is discussed by matching interior solution,outer solution and boundary solutions of the problem.And the asymptotic expansion of solution is obtained. |
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| Keywords: | nonlinear equation boundary layer internal layer matched asymptotic expansion |
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