In this paper we discuss some thermoelastic and thermoviscoelastic models obtained from the Gurtin theory, based on the invariance of the entropy under time reversal. We derive differential systems where the temperature and the velocity are ruled by generalized versions of the Moore-Gibson-Thompson equation. In the one-dimensional case, we provide a complete analysis of the evolution, establishing an existence and uniqueness result valid for any choice of the constitutive parameters. This result turns out to be new also for the MGT equation itself. Then, under suitable assumptions on the parameters, corresponding to the subcritical regime of the system, we prove the exponential stability of the related semigroup.

中文翻译：

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MGT-热粘弹性的新方法

在本文中，我们讨论了一些从 Gurtin 理论获得的热弹性和热粘弹性模型，基于时间反转下熵的不变性。我们推导出微分系统，其中温度和速度由 Moore-Gibson-Thompson 方程的广义版本控制。在一维情况下，我们提供了对演化的完整分析，建立了对本构参数的任何选择都有效的存在性和唯一性结果。这个结果对于 MGT 方程本身来说也是新的。然后，在适当的参数假设下，对应于系统的亚临界状态，我们证明了相关半群的指数稳定性。