| 具有无穷大边界值的半线性奇摄动Neumann边值问题 |
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| 引用本文： | 胡永生,沈建和,周哲彦.具有无穷大边界值的半线性奇摄动Neumann边值问题[J].福建师范大学学报(自然科学版),2011,27(4):14-19. |
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| 作者姓名： | 胡永生 沈建和 周哲彦 |
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| 作者单位： | 1. 福建师范大学数学与计算机科学学院,福建福州 350007;福建农业职业技术学院公共教学部,福建福州 350119
2. 福建师范大学数学与计算机科学学院,福建福州,350007 |
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| 基金项目： | 福建省自然科学基金资助项目(S0650010); 福建省科技厅资助项目(2005K028) |
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| 摘 要： | 基于微分不等式方法,结合边界层校正的思想,研究了一类具有无穷大边界值的半线性奇摄动Neumann边值问题解的存在性、解的渐近近似以及渐近解的误差估计等.两个典型的算例表明:基于边界层校正思想所构造的渐近解是正确且一致有效的.
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| 关 键 词： | Neumann问题 无穷大边界值 边界层校正 微分不等式 |
Neumann Problem with Infinite Boundary Values for Singularly Perturbed Semi-linear Differential Equations |
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| HU Yong-sheng,SHEN Jian-he,ZHOU Zhe-yan.Neumann Problem with Infinite Boundary Values for Singularly Perturbed Semi-linear Differential Equations[J].Journal of Fujian Teachers University(Natural Science),2011,27(4):14-19. |
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| Authors: | HU Yong-sheng SHEN Jian-he ZHOU Zhe-yan |
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| Institution: | HU Yong-sheng1,2,SHEN Jian-he1,ZHOU Zhe-yan1(1.School of Mathematics and Computer Science,Fujian Normal University,Fuzhou 350007,China,2.Department of Public Education,Fujian Vocational College of Agriculture,Fuzhou 350119,China) |
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| Abstract: | By combining the method of differential inequality with the idea of boundary layer correction,the existence and asymptotic approximation of solution of Neumann problems with infinite boundary values for semi-linear singularly perturbed differential equations is obtained.The error estimate between the asymptotic and the exact solutions are also obtained.Two typical examples are performed to verify the correctness and uniform validity of the asymptotic solution obtained by boundary correction. |
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| Keywords: | Neumann problem infinite boundary value boundary layer correction differential inequality |
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