In this work, we study of the asymptotic behavior in the whole line of a thermoelastic structure with interfacial slip and second sound where the heat conduction is given by the Cattaneo law. We prove several polynomial decay estimates depending on the smoothness of initial data. The proof is based on the semigroup approach, the energy method by introducing a Lyapunov functional, and Fourier transform.

中文翻译：

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波速对界面滑移全线热弹性结构衰减率的影响

在这项工作中，我们研究了具有界面滑移和第二声的热弹性结构整条线的渐近行为，其中热传导由 Cattaneo 定律给出。我们根据初始数据的平滑度证明了几个多项式衰减估计。证明基于半群方法，能量方法通过引入李雅普诺夫泛函和傅立叶变换。