| 一类拟线性奇摄动方程的无穷大初值问题 |
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| 引用本文： | 王爱峰,倪明康.一类拟线性奇摄动方程的无穷大初值问题[J].吉林大学学报(理学版),2010,48(1):52-56. |
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| 作者姓名： | 王爱峰 倪明康 |
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| 作者单位： | 1. 淮阴师范学院 数学科学学院, 安徽 淮安 223001,2. 华东师范大学 理工学院数学系, 上海 200062 |
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| 基金项目： | 国家自然科学基金(批准号:10671070);;上海浦江人才计划项目基金(批准号:05PJ14040);;上海市教委E-研究院建设计划项目基金(批准号:E03004);;地理信息科学教育部重点实验室开放研究项目基金 |
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| 摘 要： | 研究一类拟线性方程无穷大解值的初值问题,先通过一个简单的变换,将其转化为吉洪诺夫方程组,然后利用边界层函数法,在一定条件下,构造其形式渐近解,证明了解的存在唯一性,并给出了该形式渐近解在整个区间上一致有效的n+1阶渐近估计.
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| 关 键 词： | 无穷大解 奇摄动 拟线性 |
| 收稿时间： | 2009-01-10 |
Infinitely-Large Initial Value Problem for a Class of Quasi-Linear Singular Perturbed Equation |
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| WANG Ai-feng,NI Ming-kang.Infinitely-Large Initial Value Problem for a Class of Quasi-Linear Singular Perturbed Equation[J].Journal of Jilin University: Sci Ed,2010,48(1):52-56. |
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| Authors: | WANG Ai-feng NI Ming-kang |
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| Institution: | 1. School of Mathematical Science, Huaiyin Normal University, Huaian 223001, Anhui Province, China|2. Department of Mathematics, School of Science and Engineering, East China Normal University, Shanghai 200062, China |
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| Abstract: | A class of infinitely-large initial value problem was considered for the quasi-linear singular perturbed equation.Via a simple transformation,this equation was transformed into Tihonov system.Under suitable conditions,we constructed its formula solution using the method of boundary functions.At the same time,the (n + 1) th order asymptotic solution of the problem was given in the whole interval. |
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| Keywords: | infinitely-large solution singular perturbation quasi-linear |
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