The present article deals with the question: how time dependent non-locality influence the domain of dependency of thermal signals in solids? In order to establish the hypothesis “domain of influence” in an isotropic medium, based on the temperature-rate dependent thermoelasticity (TRDTE) theory, a thermodynamic consistent model is formulated by incorporating memory-dependent derivative (MDD). Firstly, the domain of influence theorem is established followed by a domain of dependence inequality and it certifies that for a finite time $t>0$ a solution of a given thermo-dynamical problem, corresponding to the data defined in a bounded support, vanishes outside a suitably defined bounded domain ${\mathcal{D}}^{\text{*}}\left(t\right)$. It physically interprets that an initial perturbation of a bounded thermo-elastic domain generates thermal signals which for any $t>0$ can not occupy the whole space, i.e. it propagates with a finite speed. Finally, a two-dimensional thermoelastic problem in the isotropic medium is considered for a supporting visualization of the domain of influence theorem of the memory-dependent generalized thermoelasticity theory.

本文讨论的问题是：时间相关的非局部性如何影响固体中热信号的相关性域？为了在各向同性介质中建立假设的“影响域”，基于温度速率相关的热弹性（TRDTE）理论，通过结合记忆相关导数（MDD）来构建热力学一致性模型。首先，建立影响定理的域，然后建立依赖不等式的域，并证明它在有限时间内$Ť>0$ 给定热力学问题的解决方案，对应于有界支撑中定义的数据，在合适定义的有界域之外消失 ${\mathcal{d}}^{\text{*}}（Ť）$。它从物理上解释为，有限热弹性域的初始扰动会产生热信号，对于任何$Ť>0$不能占据整个空间，即它以有限的速度传播。最后，考虑各向同性介质中的二维热弹性问题，以支持可视化依赖于记忆的广义热弹性理论的影响定理。