SOME STABILITY RESULTS FOR TIMOSHENKO SYSTEMS WITH COOPERATIVE FRICTIONAL AND INFINITE-MEMORY DAMPINGS IN THE DISPLACEMENT  

作　　者：Aissa GUESMIA Salim MESSA O UDI 

机构地区：[1]Department of Mathematics and Statistics, College of Sciences, King Fahd University of Petroleum and Minerals, P.O. Box 5005, Dhahran 31261, Saudi Arabia [2]Institut Elie cartan de Lorraine, UMR 7502, Universitd de Lorraine, Bat. A, Ile du Saulcy, 57045 Metz Cedex 01, France

出　　处：《Acta Mathematica Scientia》2016年第1期1-33,共33页数学物理学报（B辑英文版）

基　　金：funded by KFUPM under the scientific project IN141015

摘　　要：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.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.

关 键 词：WELL-POSEDNESS DECAY damping TIMOSHENKO THERMOELASTICITY 

分 类 号：O313.5[理学—一般力学与力学基础]