Electron. J. Differential Equations, Vol. 2018 (2018), No. 75, pp. 1-27.

Energy decay in a Timoshenko-type system for thermoelasticity of type III with distributed delay and past history

Jianghao Hao, Fei Wang

Abstract:
In this work, we consider a one-dimensional Timoshenko system of thermoelasticity of type III with past history and distributive delay. It is known that an arbitrarily small delay may be the source of instability. We establish the well-posedness and the stability of the system for the cases of equal and nonequal speeds of wave propagation respectively. Our results show that the damping effect is strong enough to uniformly stabilize the system even in the presence of time delay under suitable conditions and improve the related results.

Submitted May 11, 2017. Published March 17, 2018.
Math Subject Classifications: 35L70, 35L75, 93D20.
Key Words: Timoshenko system; past history; relaxation function; distributed delay; energy decay.

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Jianghao Hao
School of Mathematical Sciences
Shanxi University
Taiyuan, Shanxi 030006, China
email: hjhao@sxu.edu.cn
Fei Wang
School of Mathematical Sciences
Shanxi University
Taiyuan, Shanxi 030006, China
email: 2930904441@qq.com

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