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具有不连续源的弱非线性奇摄动边值问题 被引量：1

Weak nonlinear singular perturbed boundary value problems with discontinous source terms
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摘要 用边界层函数法讨论了具有不连续源的弱非线性奇摄动边值问题,分区间构造了它的形式渐近解,并通过缝接法对轨道进行连续缝接,在整个区间上证明了解的存在惟一性和渐近解的一致有效性,最后用数值计算验证了结论。 A class of weak nonlinear singularly perturbed boundary value problems with discontinuous source terms is examined.Using the method of boundary functions and smooth sewing orbit,the asymptotic solution of this problem is given and shown to be uniformly effective.The existence and uniqueness of the solution for the system is proved.A numerical result illustrats to the theoretical result.
作者 丁海云 倪明康
机构地区 华东师范大学数学系 上海海事大学数学系 上海高校计算科学E-研究院上海交通大学研究所
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2012年第2期8-13,共6页 Journal of Shandong University(Natural Science)
基金 上海国家科学基金会资助项目(10ZR1409200) 上海市教育委员会E-研究院建设项目(E03004) 上海市重点学科建设项目(B407)
关键词 奇摄动 渐近级数 边界层函数法 微分流形 singular perturbation asymptotic expansion boundary layer function invariable manifold
分类号 O175.14 [理学—基础数学]
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参考文献7

  • 1VASIL'EVA A B, BUTUZOV V F, KALACHEV L V. The boundary function method for singular perturbation problems [M]. Philadelphia: SIAM, 1995.
  • 2VASIL'EVA A B, BUTUZOV V F. Asymptotic expansions of solutions of singularly perturbed equations [ M]. Nauka: Mos- cow, 1973.
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  • 4丁海云,倪明康.函数不连续的二阶拟线性奇摄动边值问题[J].纯粹数学与应用数学,2010,26(5):768-775. 被引量：5
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二级参考文献5

  • 1Vasil'VA A B,Butuzov V F,Kalachev L V.The Boundary Function Method for Singular Perturbation Problems[M].Philadelphia:SIAM,1995.
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共引文献5

同被引文献9

  • 1周明儒,杜增吉,王广瓦.奇异摄动中的微分不等式理论[M].北京:科学出版社,2012:168-179.
  • 2莫嘉琪.关于非线性方程EⅣ”=,(z,Y,Y’,E)奇异摄动边值问题解的估计[J].数学年刊,1984,5A(1):73-77.
  • 3MO J Q. Generalized solution of singularly perturbed problems for nonlinear reaction diffusion equation [J]. Journal of Anhui Normal University(Natural Science), 2014, 2: 103-107.
  • 4MIKHAILOV M, OZISIK M. Unified Analysis and Solution of Heat and Mass Diffusion[M]. New York: Dover 1994.
  • 5DE FALCO C, O'RIORDAN E. Interior layers in a reaction-diffusion equation with a discontinuous diffusion coefficient [J]. Int J Numer Anal Model, 2010, 7: 444-461.
  • 6XIE F. An interface problem with singular perturbation on a subinterval [J]. Boundary Value Problems, 2014, 2014: 201.
  • 7LIN H X, XIE F. Singularly perturbed second order semilinear boundary value problems with interface conditions [J]. Boundary Value Problems, 2015, 2015: 47.
  • 8KELLY W G, PETERSON A C. The Theory of Differential Equations [M]. New York: Springer-Verlag, 2010.
  • 9杜增吉,莫嘉琪.一类扰动发展方程近似解[J].物理学报,2012,61(15):338-342. 被引量：2

引证文献1

山东大学学报（理学版）
2012年 第2期

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