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

doi:10.1016/S0252-9602(15)30075-8

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

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

Aissa GUESMIA^1,2, Salim MESSAOUDI¹

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 GUESMIA^1,2, Salim MESSAOUDI¹

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/Abstract

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:

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

中图分类号:

35B37

Aissa GUESMIA, Salim MESSAOUDI. SOME STABILITY RESULTS FOR TIMOSHENKO SYSTEMS WITH COOPERATIVE FRICTIONAL AND INFINITE-MEMORY DAMPINGS IN THE DISPLACEMENT[J]. 数学物理学报(英文版), 2016, 36(1): 1-33.

Aissa GUESMIA, Salim MESSAOUDI. SOME STABILITY RESULTS FOR TIMOSHENKO SYSTEMS WITH COOPERATIVE FRICTIONAL AND INFINITE-MEMORY DAMPINGS IN THE DISPLACEMENT[J]. Acta mathematica scientia,Series B, 2016, 36(1): 1-33.

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

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

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