We consider different models of thermoelastic plates in a bounded reference configuration: with Fourier heat conduction or with the Cattaneo model, and with or without inertial term. Some models exhibit exponential stability, others are not exponential stable. In the cases of exponential stability, we give an explicit estimate for the rate of decay in terms of the essential parameters appearing (delay \(\tau \ge 0\), inertial constant \(\mu \ge 0\)). This is first done using multiplier methods directly in \(L^2\)-spaces, then, second, with eigenfunction expansions imitating Fourier transform techniques used for related Cauchy problems; also here essentially energy estimates are used, a spectral analysis is avoided. The explicit estimates allow for a comparison. The singular limits \(\tau \rightarrow 0\), and \(\mu \rightarrow 0\) are also investigated in order to understand the mutual relevance for the (non-) exponential stability of the models. Numerical simulations underline the results obtained analytically, and exhibit interesting coincidences of analytical and numerical estimates, respectively.

我们在有界参考配置中考虑不同的热弹性板模型：具有傅立叶热传导或 Cattaneo 模型，以及有或没有惯性项。一些模型表现出指数稳定性，而另一些则不是指数稳定的。在指数稳定性的情况下，我们根据出现的基本参数（延迟\(\tau \ge 0\)，惯性常数\(\mu \ge 0\)）给出衰减率的明确估计。这首先在\(L^2\) 中直接使用乘法器方法完成-空间，然后，其次，具有模仿用于相关柯西问题的傅立叶变换技术的特征函数扩展；此处也主要使用能量估计，避免了频谱分析。明确的估计允许进行比较。还研究了奇异极限\(\tau \rightarrow 0\)和\(\mu \rightarrow 0\)以了解模型的（非）指数稳定性的相互相关性。数值模拟强调了分析获得的结果，并分别展示了有趣的分析和数值估计的巧合。