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一类奇摄动三阶常微分方程组的两点边值问题 被引量：3

Boundary value problem of a class of third order differential equations
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摘要 利用边界层函数法构造了一类奇摄动三阶方程组两点边值问题的渐近解,并严格证明了解的存在惟一性及其渐近解的一致有效性. This paper, using the method of boundary functions, studied boundary value problem of a class of singularly perturbed third order differential equations. At the same time the asymptotic solution of the problem was given and the uniform validity of its asymptotic solution was proved in a rigorous way.
作者 徐洁 陈丽华 倪明康
机构地区 华东师范大学数学系 福建师范大学福清分校
出处 《华东师范大学学报（自然科学版）》 CAS CSCD 北大核心 2008年第3期21-29,36,共10页 Journal of East China Normal University(Natural Science)
基金 国家自然科学基金(10671070) 上海市教育委员会E-研究院建设资助项目(E03004) 上海市浦江人才计划(05PJ14040) 地理信息科学教育部重点实验室开放课题
关键词 奇摄动 渐近展开 边界层函数 不变流形 singular perturbation asymptotic expansion boundary layer function unchangeable manifold
分类号 O175.1 [理学—基础数学]
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参考文献6

  • 1HOWES F A. The asymptotic solution of a class of third-order boundary value problems arising in the theory of thin film flows[J]. SIAM J Appl Math, 1983,43 (5) : 993-1004.
  • 2汪志鸣,王隔霞,林武忠.薄层流中的一类三阶奇摄动边值问题的渐近分析[J].应用数学学报,2006,29(4):699-706. 被引量：5
  • 3VASIL'VA A B, BUTUZOV V F,KALACHEV L V. The boundary function method for singular perturbation problems[J]. Philadelphia: SIAM, 1995.
  • 4VASIL'VA A B, BUTUZOV V F. Asymptotic Expansions of Solutions of Singularly Perturbed Equations[M]. Nauka: Moscow, 1973.
  • 5HORN R A,JOHSON C R. Topics in Matrix Analysis[M]. Cambridge: Cambridge University Press, 1991 : 459-489.
  • 6ESIPOVA V A. Asymptotic properties of general boundary value problems for singularly perturbed conditionally stable systems of ordinary differential equations[J]. Differential Equations,1975,11(11) : 1 457-1465.

二级参考文献15

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共引文献4

同被引文献21

引证文献3

二级引证文献4

华东师范大学学报（自然科学版）
2008年 第3期

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