In this paper, we propose a system of equations governing the dual-phase-lag heat conduction with microtemperatures. Several conditions on the coefficients are imposed so that the energy of the system is positive definite and dissipative. On this base we prove the well-posedness and exponential stability of the system by means of the semigroup theory and frequency domain method.

中文翻译：

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具有微温的双相滞后热传导

在本文中，我们提出了一个控制微温双相滞后热传导的方程组。对系数施加了几个条件，以便系统的能量是正定的和耗散的。在此基础上，利用半群理论和频域方法证明了系统的适定性和指数稳定性。