Abstract We consider a viscoelastic plate equation of Moore-Gibson-Thompson type coupled with two different kinds of thermal laws, namely, the usual Fourier one and the heat conduction law of type III. In both cases, the resulting system is shown to generate a contraction semigroup of solutions on a suitable Hilbert space. Then we prove that these semigroups are analytic, despite the fact that the semigroup generated by the mechanical equation alone does not share the same property. This means that the coupling with the heat equation produces a regularizing effect on the dynamics, implying in particular the impossibility of the localization of solutions. As a byproduct of our main result, the exponential stability of the semigroups is established.

中文翻译：

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带热传导的MGT-粘弹性板的解析性

摘要 我们考虑了一个Moore-Gibson-Thompson 类型的粘弹性板方程，它结合了两种不同的热定律，即通常的傅里叶定律和III 型热传导定律。在这两种情况下，结果系统都显示出在合适的希尔伯特空间上生成解决方案的收缩半群。然后我们证明这些半群是解析的，尽管单独由力学方程产生的半群并不具有相同的性质。这意味着与热方程的耦合对动力学产生了正则化效应，尤其意味着解的局部化是不可能的。作为我们主要结果的副产品，半群的指数稳定性成立。