The problem of description of quasi-static behavior is studied for a planar thermoelastic body incorporating an inhomogeneity, which geometrically is a strip with a small cross-section. This problem contains a small positive parameter [Formula: see text] describing the thickness of the inhomogeneity, i.e., the size of the cross-section. Relying on the variational formulation of the problem, we investigate the behavior of solutions as [Formula: see text] tends to zero. As the result, by the version of the method of formal asymptotic expansions, we derive a closed limit model in which the inhomogeneity is thin (of zero width). After this, using the Galerkin method and the classical techniques of derivation of energy estimates, we prove existence, uniqueness, and stability of a weak solution to this model.

中文翻译：

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由薄热弹性夹杂物增强的热弹性体的准静态模型

研究了包含不均匀性的平面热弹性体的准静态行为描述问题，该热弹性体在几何上是具有小横截面的条带。这个问题包含一个小的正参数[公式：见正文]描述不均匀性的厚度，即横截面的大小。依靠问题的变分公式，我们研究了当[公式：参见文本]趋于零时解的行为。结果，通过形式渐近展开方法的版本，我们推导出一个闭极限模型，其中不均匀性很薄（零宽度）。之后，利用伽辽金方法和经典的能量估计推导技术，我们证明了该模型弱解的存在性、唯一性和稳定性。