华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (3): 99-112.

• 应用数学与基础数学 • 上一篇    下一篇

耦合动力学方程的非线性特征值渐近求解

侯磊1,2, 张家健1,仇璘2,3   

  1. 1. 上海大学;数学系, 上海 200444;2.上海高校计算科学E-研究院;上海交通大学研究所,上海 200030; 3. 上海交通大学数学系, 上海 200240
  • 收稿日期:2009-10-14 修回日期:2009-12-15 出版日期:2010-05-25 发布日期:2010-05-25
  • 通讯作者: 侯磊

Asymptotic solutions of the nonlinear eigenvalue problems in the multi-fieldcoupled dynamic equations

HOU Lei1,2 ,ZHANG Jia-jian1, QIU Lin2,3   

  1. 1. Department of Mathematics, Shanghai University,Shanghai 200444, China; 2. Computational Sciences, E-Institute of Shanghai Universities at SJTU,Shanghai 200240, China; 3. Department of Mathematics, Shanghai Jiao Tong University,Shanghai 200240,China
  • Received:2009-10-14 Revised:2009-12-15 Online:2010-05-25 Published:2010-05-25
  • Contact: HOU Lei

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摘要： 介绍由约束场和受重力影响的对流扰动耦合而成的衰减平衡向量场动力学方程的特征值渐近求解.
通过引进新的参数,将一个复杂的三维约束耦合动力学特征方程转化成复空间里一维的边界层问题.通过进一步分析计算非线性特征值问题并 做了渐近摄动分析,最后给出多场耦合中扰动问题的特征值边界层解法.

关键词: 边界层分析, 渐近摄动, 非线性特征值, 边界层分析, 渐近摄动, 非线性特征值

Abstract: This article solved the asymptotic solution of the eigenvalue problem in the
dissipative equilibrium vector field of the coupled convection disturbance kinetic
equations under the constraind filed and the gravity. The approach is to use the new parameters to reduce the three-dimensional coupling dynamic equations into a one-dimensional complex space of boundary-layer. Further analysis and computing were given on the asymptotic solutions for the nonlinear eigenvalue problem. Finally, a boundary-layer eigenvalue analysis was performed to solve the field coupling perturbation in this paper.

Key words: asymptotic perturbation, nonlinear eigenvalue, boundary-layer analysis, asymptotic perturbation, nonlinear eigenvalue

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