Well-posedness and energy decay for Timoshenko systems with discrete time delay under frictional damping and/or infinite memory in the displacement

被引：5
作者：
Guesmia A. [1 ]
机构：
[1] Institut Elie Cartan de Lorraine (IECL), UMR 7502, Université de Lorraine, Bat. A, Ile du Saulcy, Metz Cedex 01
来源：
Afrika Matematika | 2017年 / 28卷 / 7-8期
关键词：
Energy method; Frictional damping; General decay; Infinite memory; Semigroup theory; Time delay; Timoshenko-type; Viscoelastic; Well-posedness;
D O I：
10.1007/s13370-017-0514-8
中图分类号：
学科分类号：
摘要：
In this paper, we consider a vibrating system of Timoshenko-type in a bounded one-dimensional domain with discrete time delay and complementary frictional damping and infinite memory controls all acting on the transversal displacement. We show that the system is well-posed in the sens of semigroup and that, under appropriate assumptions on the weights of the delay and the history data, the stability of the system holds in case of the equal-speed propagation as well as in the opposite case in spite of the presence of a discrete time delay, where the decay rate of solutions is given in terms of the smoothness of the initial data and the growth of the relaxation kernel at infinity. The results of this paper extend the ones obtained by the present author and Messaoudi in (Acta Math Sci 36:1–33, 2016) to the case of presence of discrete delay. © 2017, African Mathematical Union and Springer-Verlag GmbH Deutschland.
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页码：1253 / 1284
页数：31
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