In this study, we approach the strain gradient thermoelasticity of bodies with microtemperatures. We define the internal energy corresponding to an arbitrary solution of the mixed problem with boundary and initial values, considered in the context of strain gradient thermoelasticity of bodies with microtemperatures. The Cesaro means of different parts of the internal energy are considered. In our main result, we prove the asymptotic equipartition of the strain and kinetic energies, in the case \(t\rightarrow \infty \).

中文翻译：

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微观温度下体在应变梯度热弹性中的能量行为

在这项研究中，我们用微观温度处理物体的应变梯度热弹性。我们定义了与边界和初始值混合问题的任意解相对应的内部能量，考虑了具有微小温度的物体的应变梯度热弹性。考虑了内部能量不同部分的Cesaro均值。在我们的主要结果中，在\（t \ rightarrow \ infty \）的情况下，我们证明了应变和动能的渐近均分。