In the last twenty years, the analysis of problems involving dual-phase-lag models has received an increasing attention. In this work, we consider the coupling between one of these models and the microtemperatures effects. In order to overcome the infinite speed paradox, two relaxation parameters are introduced for each evolution equation related to the temperature and the microtemperatures, leading to a system of linear hyperbolic partial differential equations. Its variational formulation is written in terms of the temperature acceleration and the microtemperatures acceleration. An energy decay property is proved. Next, fully discrete approximations are introduced by using the finite element method and the Euler scheme, proving a stability property and a discrete version of the energy decay, obtaining a priori error estimates and performing one- and two-dimensional numerical simulations.

在过去的二十年中，涉及双相滞后模型的问题的分析受到越来越多的关注。在这项工作中，我们考虑了这些模型之一与微观温度效应之间的耦合。为了克服无限速度悖论，针对与温度和微观温度有关的每个演化方程引入了两个松弛参数，从而形成了线性双曲型偏微分方程组。它的变化形式用温度加速度和微温度加速度来表示。证明了能量衰减特性。接下来，通过使用有限元方法和Euler方案引入完全离散的近似值，证明了稳定性和能量衰减的离散形式，