Some stability results for timoshenko systems with cooperative frictional and infinite-memory dampings in the displacement

详细信息    查看全文

• 作者：Aissa GUESMIA^a ; ^b ; ^{guesmia@kfupm.edu.sa" class="auth_mail" title="E-mail the corresponding author} ; ^{aissa.guesmia@univ-lorraine.fr" class="auth_mail" title="E-mail the corresponding author} ; Salim MESSAOUDI^a ; ^{messaoud@kfupm.edu.sa" class="auth_mail" title="E-mail the corresponding author}
• 关键词：well-posedness ; decay ; damping ; Timoshenko ; thermoelasticity
• 刊名：Acta Mathematica Scientia
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：36
• 期：1
• 页码：1-33
• 全文大小：389 K

文摘

In this paper, we consider a vibrating system of Timoshenko-type in a one-dimensional bounded domain with complementary frictional damping and infinite memory acting on the transversal displacement. We show that the dissipation generated by these two complementary controls guarantees the stability of the system in case of the equal-speed propagation as well as in the opposite case. We establish in each case a general decay estimate of the solutions. In the particular case when the wave propagation speeds are different and the frictional damping is linear, we give a relationship between the smoothness of the initial data and the decay rate of the solutions. By the end of the paper, we discuss some applications to other Timoshenko-type systems.