TY - GEN
T1 - Dynamic behavior of a one-dimensional thermoviscoelastic system
AU - Wang, Jing
AU - Wang, Jun Min
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/7/17
Y1 - 2015/7/17
N2 - In this paper, we study the dynamic behavior of a one-dimensional linear thermoviscoelastic system with Dirichlet boundary conditions. A remarkable characteristic is that the system operator is not of compact resolvent. Using the asymptotic analysis technique, it is shown that there are three branches of eigenvalues: two of them are along the negative real axis approaching-∞ and another branch, distributing on the negative real axis, converges to a negative real point which is the unique continuous spectrum. Moreover, the set of generalized eigenfunctions forms a Riesz basis for the energy state space. Consequently, the spectrum-determined growth condition holds true, and an exponential stability is concluded. Finally, some numerical simulations are presented.
AB - In this paper, we study the dynamic behavior of a one-dimensional linear thermoviscoelastic system with Dirichlet boundary conditions. A remarkable characteristic is that the system operator is not of compact resolvent. Using the asymptotic analysis technique, it is shown that there are three branches of eigenvalues: two of them are along the negative real axis approaching-∞ and another branch, distributing on the negative real axis, converges to a negative real point which is the unique continuous spectrum. Moreover, the set of generalized eigenfunctions forms a Riesz basis for the energy state space. Consequently, the spectrum-determined growth condition holds true, and an exponential stability is concluded. Finally, some numerical simulations are presented.
KW - Asymptotic analysis
KW - Riesz basis
KW - Stability
KW - Thermoviscoelastic system
UR - http://www.scopus.com/inward/record.url?scp=84945568277&partnerID=8YFLogxK
U2 - 10.1109/CCDC.2015.7162260
DO - 10.1109/CCDC.2015.7162260
M3 - Conference contribution
AN - SCOPUS:84945568277
T3 - Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015
SP - 2061
EP - 2066
BT - Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 27th Chinese Control and Decision Conference, CCDC 2015
Y2 - 23 May 2015 through 25 May 2015
ER -