TY - JOUR
T1 - EXPONENTIAL AND POLYNOMIAL STABILIZATION OF LAMINATED BEAMS WITH TWO HISTORY MEMORIES
AU - Méndez, Teófanes Quispe
AU - Cabanillas Zannini, V. R.
AU - Feng, Baowei
N1 - Publisher Copyright:
© 2023, American Institute of Mathematical Sciences. All rights reserved.
PY - 2023/12
Y1 - 2023/12
N2 - In this paper, a laminated beam system with two history-type controls is studied. One of the controls acts on the effective rotation angle and the other on the slip equation. The latter control replaces the structural damping usually considered in this model in the literature. Using the semi-group of linear operators approach, we prove the system is globally well-posed. We establish the exponential stability of the system provided the equal-speed waves propagation holds. Otherwise, the system lacks exponential stability. The polynomial decay with rate t− 41 is also proved using the theorem due to Borichev and Tomilov.
AB - In this paper, a laminated beam system with two history-type controls is studied. One of the controls acts on the effective rotation angle and the other on the slip equation. The latter control replaces the structural damping usually considered in this model in the literature. Using the semi-group of linear operators approach, we prove the system is globally well-posed. We establish the exponential stability of the system provided the equal-speed waves propagation holds. Otherwise, the system lacks exponential stability. The polynomial decay with rate t− 41 is also proved using the theorem due to Borichev and Tomilov.
KW - history memory
KW - Laminated beam
KW - semigroup
KW - stability
KW - Timoshenko beam
UR - http://www.scopus.com/inward/record.url?scp=85165897954&partnerID=8YFLogxK
U2 - 10.3934/mcrf.2022037
DO - 10.3934/mcrf.2022037
M3 - Artículo (Contribución a Revista)
AN - SCOPUS:85165897954
SN - 2156-8472
VL - 13
SP - 1258
EP - 1281
JO - Mathematical Control and Related Fields
JF - Mathematical Control and Related Fields
IS - 4
ER -