一类时滞方程的谱与解展开

Abstract

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

CLC Number:

39B99

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

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