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 ...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 initiM data and the decay rate of the solutions. By the end of the paper, we discuss some applications to other Timoshenko-type systems.展开更多
基金funded by KFUPM under the scientific project IN141015
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 initiM data and the decay rate of the solutions. By the end of the paper, we discuss some applications to other Timoshenko-type systems.
