In this paper, we investigate one-dimensional thermoelastic system of Timoshenko type III with double memory dampings. At first we give the global existence of solutions by using semigroup theory. Then we can prove the energy decay of solutions by constructing a series of Lyapunov functionals and obtain the existence of absorbing ball. Finally, we prove the asymptotic compactness by using uniform contractive functions and obtain the existence of uniform attractor.

中文翻译：

---

具有弱阻尼的III类非自治Timoshenko系统的整体存在，渐近行为和一致吸引子

在本文中，我们研究具有双重记忆阻尼的Timoshenko III型一维热弹性系统。首先，我们使用半群理论给出了解的整体存在性。然后我们可以通过构造一系列Lyapunov泛函来证明解的能量衰减，并获得吸收球的存在。最后，我们利用均匀的收缩函数证明了渐近紧性，并获得了均匀吸引子的存在性。