Title :
On dynamic behavior of a hyperbolic thermoelastic system with memory type in terms of eigenfrequencies
Author :
Wang, Jun-Min ; Guo, Bao-Zhu
Author_Institution :
Dept. of Math., Beijing Inst. of Technol.
Abstract :
This paper studies the dynamic behavior of a one-dimensional thermoelastic system with memory type in terms of its eigenfrequencies. The asymptotic expansions for eigenvalues and eigenfunctions are derived. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. From this, we deduce the spectrum-determined growth condition, and as a consequence, the exponential stability of the system is concluded
Keywords :
Hilbert spaces; asymptotic stability; eigenvalues and eigenfunctions; nonlinear dynamical systems; state-space methods; thermoelasticity; 1D thermoelastic system; Hilbert state space; Riesz basis; asymptotic expansion; dynamic behavior; eigenfrequencies; eigenfunctions; eigenvalues; exponential stability; hyperbolic thermoelastic system; memory type; spectrum-determined growth condition; Africa; Eigenvalues and eigenfunctions; Hilbert space; Mathematics; Partial differential equations; Stability; State-space methods; Temperature; Thermal conductivity; Thermoelasticity;
Conference_Titel :
American Control Conference, 2006
Conference_Location :
Minneapolis, MN
Print_ISBN :
1-4244-0209-3
Electronic_ISBN :
1-4244-0209-3
DOI :
10.1109/ACC.2006.1655452
