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应用数学学报  2013, Vol. 36 Issue (2): 306-314    DOI:
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一类带非线性无穷大边界值条件的二阶半线性方程奇摄动问题
胡永生1,2, 沈建和1, 周哲彦1
1. 福建师范大学数学与计算机科学学院, 福州, 350007;
2. 福建农业职业技术学院, 福州, 350119
A Second-order Semi-linear Equation’s Singularly Perturbed Problem with Nonlinear and Infinite Boundary Value Conditions
HU Yongsheng1,2, SHEN Jianhe1, ZHOU Zheyan1
1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007;
2. Department of Public Education, Fujian Vocational College of Agriculture, FuZhou, 350119
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摘要 研究了一类带非线性无穷大边界值条件的二阶半线性方程的奇摄动边值问题. 利用边界层函数法, 分别构造了左、右边界层的校正函数(含指数型和代数型), 得到了奇摄动问题解的渐近行为; 根据微分不等式理论, 证明了该问题解的存在性, 并给出了退化解与精确解的误差估计. 通过与数值积分解进行比较, 一个典型的算例验证了本文理论结果的正确性.
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胡永生
沈建和
周哲彦
关键词无穷大边界值   非线性边界条件   半线性方程   奇摄动   微分不等式理论     
Abstract: A second-order semi-linear equation's singularly perturbed boundary value problem with nonlinear and infinite boundary value conditions is studied in this paper. By making use of the method of boundary layer functions, the correction functions of the left and right boundary layers, including the exponential and algebra-tic types, are constructed. Thus, the uniformly valid asymptotic solution is derived. Then, based on the theory of the differential inequality, existence of solutions of the boundary value problem is proved and the error estimation between the reduced and the exact solutions is given. By comparing with the numerical integration solution, a typical example is deduced for verifying the correctness of the theoretical result.
Key wordsinfinite boundary values   nonlinear boundary conditions   semi-linear equation singular perturbation   the theory of the differential inequality   
收稿日期: 2011-01-25;
基金资助:国家自然科学基金(11201072,11102041);福建省教育厅A类(JA10065)资助项目.
引用本文:   
胡永生,沈建和,周哲彦. 一类带非线性无穷大边界值条件的二阶半线性方程奇摄动问题[J]. 应用数学学报, 2013, 36(2): 306-314.
HU Yongsheng,SHEN Jianhe,ZHOU Zheyan. A Second-order Semi-linear Equation’s Singularly Perturbed Problem with Nonlinear and Infinite Boundary Value Conditions[J]. Acta Mathematicae Applicatae Sinica, 2013, 36(2): 306-314.
 
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