期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

一个带有小参数的二维椭圆方程的渐近性分析

The Asymptotic Property Analysis to a 2-D Elliptic Equations with Small Parameters
原文传递
导出
摘要 通过数值方法研究在边界充分(逐段)光滑区域上的带有小参数的二维椭圆方程在部分Dirichlet边界控制下的渐近性问题.对于一维的情形求解析解的结果,对高维问题提出类似的问题.但高维问题解析求解一般不可能,因此采用数值分析的方法.数值结果表明,在所选的条件下,边界值对小常数仍然不是解析的. In this paper we deal with an elliptic equation with small parameters. This problem is initiated from the regularity of multi-dimensionai wave equation under partial Dirichlet control and collocated observation. We are interested in the analyticity of this function with respect to the small parameter. However, the one-dimensional analytic solution shows that this is not true. Through numerical analysis, we found that this is also not true for 2-dimensional case.
作者 王军梅 董沛武 姚翠珍
机构地区 北京理工大学管理与经济学院 北京理工大学数学学院
出处 《数学的实践与认识》 CSCD 北大核心 2012年第20期234-238,共5页 Mathematics in Practice and Theory
关键词 椭圆方程 Dirichlet边界控制 解析 有限元方法 Elliptic equation Dirichlet boundary control Numerical analysis finite elementmethod
分类号 O175.25 [理学—基础数学]
  • 相关文献

参考文献10

  • 1Curtain R F and Zwart H. an Introduction to Infinite Dimensional Linear Systems Theory[M] Springer-Verlag, New York, 1995.
  • 2Weiss G. Transfer functions of regular linear systems, part 1, characterizations of regularity[J] Trans. AMS, 342(1994), 827-854.
  • 3Weiss G. Admissible observation operations for linear semigroups[J]. Isreal J Math, 1989(65): 19-43.
  • 4Ammari K and Tucsnak M. Stabilization of second order evolution equations by a class of unbounded feedbacks[J]. ESIAM Control & Optim Calc Var 2001(6): 361-386.
  • 5K.Ammari, Dirichlet boundary stabilization of the wave equation, Asymptotic Analysis, 2002, 30(2): 117-130.
  • 6殷杰,姚翠珍.二维波动方程部分Dirichlet边界控制正则性的数值分析[J].数学的实践与认识,2005,35(5):190-193. 被引量：1
  • 7Byrnes C I, Gilliam D S, Shubov B I, Weiss G. Regular linear systems governed by a boundary controlled heat equation[J]. Journal of Dynamic Control systems, 2002(8): 341-370.
  • 8Guo B Z, Phung K D, Zhang X. On the regularity of wave equation with collocated partial Dirichlet control and observation[J]. Preprint, Academy of math and system sciences, 2004.
  • 9Guo B Z and Xu C Z. Regularity of the transfer function of a wave equation in a disk with Dirichlet collocated boundary control and observation[J], manuscript, 2002.
  • 10谢宇,郭宝珠.弹性弦Dirichlet边界反馈控制的镇定与Riesz基生成[J].数学的实践与认识,2003,33(3):99-108. 被引量：4

二级参考文献23

  • 1Ammari K. Dirichlet boundary stabilization of the wave equation[J]. Asymptotic Analysis, 2002. 30(2): 117--130.
  • 2Ammari K. Tucsnak M. Stabilization of second order evolution equations by a class of unbounded feedbacks[J].ESAIM Control Optim Calc Var. 2001. 6: 361--386.
  • 3Chen G, Coleman M. West H H. Pointwise stabilization in the middle of the span for second order systems.nonuniform and uniform exponential decay of solutions[J]. SIAM J Appl Math, 1987, 47: 751--780.
  • 4Curtain R F, Zwart H. An Introduction to Infinite-Dimensional Linear Systems Theory[M]. Texts in Applied Mathematics 21,Springer-Verlag.New York,1995.
  • 5Curtain R F. The Salamon-Weiss class of well-posed infinite dimensional linear systems: a survey[J]. IMA J of Math Control and Inform. 1997. 14: 207--223.
  • 6Guo B Z. Luo Y H. Controllability and stability of a second order hyperbolic system with collocated sensor/actuator[J]. Systems & Control Letters, 2002. 46(1): 45--65.
  • 7Guo B Z. Rugularity of the transfer function of a wave equation in a disk with Dirichlet boundary control and collocated observation[J], manuscript. 2002.
  • 8Guo B Z. Riesz basis approach to the stabilization of a flexible beam with a tip mass[J]. SIAM J Control & Optim,2001. 39: 1736--1747.
  • 9Lions J L. Exact controlability, stabilization and perturbations for distributed systems[J]. SIAM Review. 1988.30 : 1--68.
  • 10Pritchard A J. Wirth A. Unbounded control and observation systems and their duality[J]. SIAM J Control & Optim. 1978. 16: 535--545.

共引文献3

数学的实践与认识
2012年 第20期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部