In this paper, we consider the Cauchy problem related to the standard linear solid model with Gurtin–Pipkin thermal law in the whole space. Under some assumptions on the relaxation function g, we establish the well-posedness result by using semigroup theory. Besides, by using the energy method in the Fourier space, we prove the decay estimate result under the non-critical case. Our result indicates that the decay property is of the regularity-loss type, which is in line with the decay property of Cattaneo system.

中文翻译：

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Gurtin-Pipkin热定律的标准线性固体模型Cauchy问题的正则损失型的适定性和衰减性质

在本文中，我们考虑了与在整个空间中具有Gurtin-Pipkin热定律的标准线性实体模型有关的Cauchy问题。在关于松弛函数g的一些假设下，我们使用半群理论建立了适定性结果。此外，通过在傅立叶空间中使用能量方法，我们证明了在非临界情况下的衰减估计结果。我们的结果表明，衰变性质属于规律损失型，与Cattaneo系统的衰变性质相符。