DocumentCode :
1704295
Title :
Exponential stability of a one-dimensional thermoviscoelastic system with memory type
Author :
Wang Jing ; Wang Jun-Min
Author_Institution :
Sch. of Math., Beijing Inst. of Technol., Beijing, China
fYear :
2013
Firstpage :
1258
Lastpage :
1263
Abstract :
In this paper, we study the stability for a one-dimensional linear thermoviscoelastic equation with memory type for Dirichlet-Dirichlet boundary conditions. A detailed spectral analysis gives that the spectrum of the system contains two parts: the point and continuous spectrum. It is shown that there are three classes of eigenvalues: one is along the negative real axis approaching to -∞, the second is approaching to a vertical line which parallels to the imagine axis, and the third class is distributed around the continuous spectrum which are accumulation points of the last classes of eigenvalues. Moreover, it is pointed out that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the energy state space. Finally, the spectrum-determined growth condition holds true and the exponential stability of the system is then established.
Keywords :
asymptotic stability; eigenvalues and eigenfunctions; viscoelasticity; Dirichlet-Dirichlet boundary conditions; Riesz basis; continuous spectrum; eigenvalues; energy state space; exponential stability; memory type; one-dimensional thermoviscoelastic system; point spectrum; spectral analysis; spectrum-determined growth; Boundary conditions; Control theory; Damping; Eigenvalues and eigenfunctions; Equations; Spectral analysis; Stability; Asymptotic Analysis; Riesz Basis; Stability; Thermoviscoelastic System;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Control Conference (CCC), 2013 32nd Chinese
Conference_Location :
Xi´an
Type :
conf
Filename :
6639620
Link To Document :
بازگشت