期刊文献+

用微分不等式对二次方程奇摄动问题解的估计 被引量:5

The estimation of solution for singularly perturbed problems of second degree equation via differential inequality
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摘要 利用微分不等式对二次方程奇异摄动问题的解作出了估计,得出了本问题任意阶的一致有效的渐近展开式. In this paper, the shift of shock position for a class of nonlinear equations is considered. The location of the shock will be larger move, even moves away from internal layer to the endpoint when the boundary conditions change smaller.
作者 冯茂春
机构地区 湖州师范学院
出处 《纯粹数学与应用数学》 CSCD 2004年第2期134-139,144,共7页 Pure and Applied Mathematics
基金 浙江省自然科学基金资助项目(102009).
关键词 非线性方程 外部解 校正项 边界层 nonlinear equation,shock,internal layer,boundary layer
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参考文献7

  • 1O'Malley R E. Introduction to singular perturbations[M]. New York : Academic Press,1974.
  • 2O'Malley R E. On a boundary value problem for a nonlinear differential equation with a small parametrer[J]. SIAN J. Appl. Math. ,1969,17:569-581.
  • 3Dorr F W,Parter S V and Shampine L F. Applications of the maximum principle to singular perturbation problems[J]. SIAM Rev. , 1973,15: 43- 88.
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  • 6莫嘉琪.关于非线性方程εy"=f(x,y,y'',ε)奇异摄动边值问题解的估计[J].数学年刊:A辑,1984,(5):73-77.
  • 7Bohé A. The shock location for a class of sensitive boundary value problems[J].J. Math.Anal. Appl.,1999,235:295-314.

共引文献2

同被引文献20

  • 1莫嘉琪.一类奇摄动边值问题解的套层现象[J].数学研究,1995,28(2):48-53. 被引量:10
  • 2汤小松.拟线性方程的奇摄动Robin问题[J].井冈山学院学报(综合版),2005,26(08M):21-23. 被引量:2
  • 3O'Malley R E Jr. Introduction to Singular Perturbations[M]. New York: Academic Press, 1974.
  • 4Dorr F W, Parter S V, Shampine L F. Applications of the maximum principle to singular perturbation problems[J]. SIAM Review, 1973, 15(1): 43-88.
  • 5莫嘉琪 冯茂春.反应扩散时滞方程的非线性摄动问题.数学物理学报,2001,21(2):254-258.
  • 6Nayfeh A H. Introduction to Perturbed Techniques[M]. New York: John Weiley & Sons, 1981.
  • 7Howers F A. Differential ineguaities of higher order and the asymptotic solution of nonlinear boundary value problems[J]. SIAM Journal on Mathematical Analysis, 1982, 13(1): 61-79.
  • 8瓦西里耶娃,布图佐夫.奇摄动方程解的渐近展开式[M].莫斯科:科学出版社,1973.
  • 9O'Malley R E Jr..Introduction to Singular Perturbations[M].New York:Academic Press,1974.
  • 10O'Malley R E Jr..On a boundary value problem for a nonlinear differential equation with a small parameter[J].SIAN J.Appl.Math.,1969,17:569--581.

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