We consider a one-dimensional thermoelastic Timoshenko system, where the heat conduction is given by Green and Naghdi theories and acting on shear force. We prove that the unique damping given by the memory is sufficiently strong to stabilize the system exponentially, depending on a new relationship between the coefficients of the system and under some assumptions on the kernel of the memory term. In fact, we establish a general decay result, of which exponential and polynomial decay results are special cases.

中文翻译：

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具有 III 型热弹性的粘弹性型 Timoshenko 系统的一般衰减

我们考虑一维热弹性 Timoshenko 系统，其中热传导由 Green 和 Naghdi 理论给出并作用于剪切力。我们证明了内存给出的独特阻尼足够强以指数方式稳定系统，这取决于系统系数之间的新关系以及在对内存项的内核的某些假设下。事实上，我们建立了一个一般的衰减结果，其中指数和多项式衰减结果是特例。