| 一类四阶非线性方程的奇摄动边值问题 |
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| 引用本文： | 陈燕娜,欧阳成.一类四阶非线性方程的奇摄动边值问题[J].湖南工程学院学报(自然科学版),2012(1):63-65. |
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| 作者姓名： | 陈燕娜 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： | 浙江省自然科学基金资助项目(Y6110502);浙江省新世纪教改项目(ZC09063) |
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| 摘 要： | 利用匹配渐近展开法,讨论了一类四阶非线性方程的奇摄动边值问题.首先求得了该问题带有四个任意常数的外部解;其次引进伸长变量,根据边界条件与匹配原则,确定了左右边界层附近的内部解及外部解;最后得到了该问题的渐近解.
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| 关 键 词： | 奇摄动 非线性 边界层 渐近解 |
A Class of Singularly Perturbed Boundanry Value Problems for Fourth-order Nonlinear Equation |
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| CHEN Yan-na,OU YANG Cheng.A Class of Singularly Perturbed Boundanry Value Problems for Fourth-order Nonlinear Equation[J].Journal of Hunan Institute of Engineering(Natural Science Edition),2012(1):63-65. |
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| Authors: | CHEN Yan-na OU YANG Cheng |
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| Institution: | (Department of Mathematics,Huzhou Teachers College,Huzhou 313000,China) |
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| Abstract: | Using the matching asymptotic expansion method,a class of singularly perturbed boundary value problems for forth-order nonlinear equation is studied.Firstly,the outer solution with four arbitrary constants of the problem is solved;secondly,introducing the stretched variables,according to the boundary conditions and the matching rule,the outer solution and the interior solutions near the left and right boundary layers are determined.Finally,the asymptotic solution of the problem is obtained. |
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| Keywords: | singular perturbation nonlinear boundary layer asymptotic solution |
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