数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 1-33.doi: 10.1016/S0252-9602(15)30075-8

• 论文 •    下一篇

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

Aissa GUESMIA1,2, Salim MESSAOUDI1   

  1. 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, Université de Lorraine, Bat. A, Ile du Saulcy, 57045 Metz Cedex 01, France
  • 收稿日期:2014-09-09 修回日期:2015-02-26 出版日期:2016-01-30 发布日期:2016-01-30
  • 通讯作者: Salim MESSAOUDI,E-mail:messaoud@kfupm.edu.sa E-mail:messaoud@kfupm.edu.sa
  • 作者简介:Aissa GUESMIA,E-mail:guesmia@kfupm.edu.sa,aissa.guesmia@univ-lorraine.fr

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

Aissa GUESMIA1,2, Salim MESSAOUDI1   

  1. 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, Université de Lorraine, Bat. A, Ile du Saulcy, 57045 Metz Cedex 01, France
  • Received:2014-09-09 Revised:2015-02-26 Online:2016-01-30 Published:2016-01-30
  • Contact: Salim MESSAOUDI,E-mail:messaoud@kfupm.edu.sa E-mail:messaoud@kfupm.edu.sa

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 initial 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

Abstract:

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.

Key words: well-posedness, decay, damping, Timoshenko, thermoelasticity

中图分类号: 

  • 35B37