In the present paper we consider the Standard Linear Solid model in RN coupled with the Cattaneo law of heat conduction. We show the well-posedness and asymptotic stability of the problem, giving decay rates for a norm related to the solution. These results are compared with those given for the Fourier problem in (Pellicer and Said-Houari (2020)) and the ones of the problem without heat conduction (see previous work (Appl Math. Optim 80 (2019) 447–478)). The main difference is that the Cattaneo system exhibits the well-known regularity-loss phenomenon. The methods used to prove these results are the energy method in the Fourier space and the eigenvalues expansion method.

中文翻译：

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关于Cattaneo导热的标准线性实体模型的Cauchy问题

在本文中，我们考虑了RN中的标准线性实体模型以及Cattaneo热传导定律。我们展示了问题的适定性和渐近稳定性，给出了与解有关的范数的衰减率。将这些结果与（Pellicer和Said-Houari（2020））中的傅立叶问题以及没有传热的问题中的结果进行了比较（请参阅先前的工作（Appl Math。Optim 80（2019）447-478））。主要区别在于Cattaneo系统表现出众所周知的规则损失现象。用于证明这些结果的方法是傅立叶空间中的能量方法和特征值展开法。