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二阶半线性奇摄动边值问题解的渐近行为
引用本文:刘帅,周哲彦,沈建和.二阶半线性奇摄动边值问题解的渐近行为[J].数学物理学报(A辑),2014,34(2):437-444.
作者姓名:刘帅  周哲彦  沈建和
作者单位:福建师范大学 数学与计算机科学学院 福州 |350007
基金项目:国家自然科学基金(11201072, 11102041)、中国博士后科学基金(2011M500803)和福建省教育厅A类项目(JA10065)资助.
摘    要:该文研究非法向双曲条件下的二阶半线性奇摄动边值问题解的渐近行为.利用边界层函数法,构造了区间端点处的代数型边界层,获得了问题的一致有效渐近解;利用微分不等式理论,证明了解的存在性以及渐近解与精确解之间的误差估计.通过一个典型的算例,验证了该文的理论结果.

关 键 词:非法向双曲  边界层函数法  代数边界层  渐近行为
收稿时间:2012-09-05
修稿时间:2013-03-01

Asymptotic Behavior of Solutions for Second-Order SemilinearSingularly Perturbed Boundary Value Problem
LIU Shuai,ZHOU Zhe-Yan,SHEN Jian-He.Asymptotic Behavior of Solutions for Second-Order SemilinearSingularly Perturbed Boundary Value Problem[J].Acta Mathematica Scientia,2014,34(2):437-444.
Authors:LIU Shuai  ZHOU Zhe-Yan  SHEN Jian-He
Affiliation:School of Mathematics and Computer |Science, Fujian Normal |University, Fuzhou 350007
Abstract:In this paper, the asymptotic behavior of solutions for second-order semi-linear singularly perturbed boundary value problems without normal hyperbolicity is studied. By using the method of boundary layer function, we construct the algebraic boundary layers and hence obtain the uniformly valid asymptotic solution and give the error estimate between the asymptotic and exact solutions via the way of differential inequalities. The correctness of the theoretical result is verified through a typical examples.
Keywords:Non-hyperbolicityzz  Boundary function methodzz  Algebraic decayzz  Asymptotic solutionszz
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