| 一类四阶非线性奇摄动方程的边值问题 |
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| 引用本文： | 朱秀珠,欧阳成.一类四阶非线性奇摄动方程的边值问题[J].应用数学与计算数学学报,2012,26(2):248-252. |
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| 作者姓名： | 朱秀珠 欧阳成 |
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| 作者单位： | 湖州师范学院理学院,浙江湖州,313000 |
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| 基金项目： | 基金项目:国家自然科学基金资助项目，浙江省自然科学基金资助项目 |
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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具有两个边界层的奇摄动边值问题．引进伸长变量，根据边界条件与匹配原则，在一定的可解性条件下，给出了外部解和左右边界层附近的内层解，得到了该问题的二阶渐近解，并举例说明了这类非线性问题渐近解的存在性．
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| 关 键 词： | 边界层 非线性 奇摄动 渐近解 |
A class of boundary value problems for four-order nonlinear singular perturbation equation |
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| ZHU Xiu-zhu,OUYANG Cheng.A class of boundary value problems for four-order nonlinear singular perturbation equation[J].Communication on Applied Mathematics and Computation,2012,26(2):248-252. |
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| Authors: | ZHU Xiu-zhu OUYANG Cheng |
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| Institution: | (Faculty of Science,Huzhou Teachers College,Huzhou 313000, Zhejiang Province,China) |
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| Abstract: | Using the matching asymptotic expansion method,a class of singularly perturbed boundary value problems with two boundary layers for forth-order nonlinear equation is studied.Introducing the stretched variables,according to the boundary conditions and the matching principle,under the definite solvability conditions,the outer solution and the interior solution near the left and right boundary layers are given.The asymptotic solution with second-order for the problem is obtained.The existence of the solution for this class of nonlinear problems is illustrated by an example. |
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| Keywords: | boundary layer nonlinear singular perturbation asymptotic solution |
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