In this paper we investigate the time decay of the solutions for a thermoelastic plate with voids in the cases when the heat conduction is modeled by the Fourier law and when it is modeled by the type III theory (with and without the inertial term). In all situations we show that, in general, the strong stability holds. In particular, we show slow decay of solutions for the Fourier case, that is, the solutions do not decay exponentially to zero (in general). However, if the coefficients satisfy a new relationship involving the inertial coefficient (singular case), we characterize the exponential decay of solutions. On the other hand, for the type III theory the situation is very different and we prove that generically the solutions decay to zero exponentially. This is another striking aspect when we compare both theories. This difference is a consequence of the couplings appearing in the type III case which are not present in the case of the Fourier law.

在本文中，我们研究了在热传导由傅立叶定律建模和由 III 类理论（有和没有惯性项）建模的情况下，具有空隙的热弹性板的解的时间衰减。在所有情况下，我们表明，一般来说，强稳定性成立。特别是，我们展示了傅立叶情况下解的缓慢衰减，也就是说，解不会以指数方式衰减到零（通常）。然而，如果系数满足涉及惯性系数的新关系（奇异情况），我们表征解的指数衰减。另一方面，对于 III 类理论，情况非常不同，我们证明了一般情况下，解决方案以指数方式衰减到零。当我们比较这两种理论时，这是另一个引人注目的方面。