一类时滞方程的谱与解展开

数学物理学报 ›› 2009, Vol. 29 ›› Issue (4): 843-857.

一类时滞方程的谱与解展开

王雷, 许跟起

(天津大学数学系, 天津 300072)

收稿日期:2007-12-30 修回日期:2009-05-26 出版日期:2009-08-25 发布日期:2009-08-25
基金资助:
国家自然科学基金(60474017)资助

Spectral Analysis and Expansion of Solution to a Class of Delay Differential Equations

WANG Lei, HU Gen-Qi

(Department of Mathematics, Tianjin University, Tianjin 300072)

Received:2007-12-30 Revised:2009-05-26 Online:2009-08-25 Published:2009-08-25
Supported by:
国家自然科学基金(60474017)资助

摘要/Abstract

摘要：

该文研究一类时滞方程解的展开问题. 研究的模型来自于实际高精密切割过程中具有时间延迟的机床振动问题. 对此模型,借助于泛函分析方法,将其写成抽象发展方程. 对系统确定的算子给出了较细致的谱分析,得到本征值的渐近表达式. 同时证明相应的本征向量不能构成状态空间基, 但给出方程解的展开式.

关键词: 时滞方程, C₀半群, 谱分析, 解展开

Abstract:

In this paper, the authors investigate the spectrum and expansion of solutions for a class of delay differential equations. The model under consideration comes from a practical problem, which describes machine tool vibration in cutting process. They tranform the model into a first order differential equation in a Hilbert state space. And then using the theory of C₀ semigroup, they obtain the well-posed-ness of the sytem. By a detailed spectrum analysis, they give an explicit asymptotic expression of all eigenvalues. In addtion, they show that the eigenfunctions of the system do not form a basis for the state space; however, they get the exspansion of solution of the system according to the eigenfunctions.

Key words: Delay differential equation, Spectrum, Solution expanssion

中图分类号:

39B99

王雷, 许跟起. 一类时滞方程的谱与解展开[J]. 数学物理学报, 2009, 29(4): 843-857.

WANG Lei, HU Gen-Qi. Spectral Analysis and Expansion of Solution to a Class of Delay Differential Equations[J]. Acta mathematica scientia,Series A, 2009, 29(4): 843-857.

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