The purpose of this paper is twofold. We first provide the mathematical analysis of a dynamic contact problem in thermoelasticity, when the contact is governed by a normal damped response function and the constitutive thermoelastic law is given by the Duhamel-Neumann relation. Under suitable hypotheses on data and using a Faedo-Galerkin strategy, we show the existence and uniqueness of solution for this problem. Then, we study the particular case when the deformable body is, in fact, a shell and use asymptotic analysis to study the convergence to a 2D limit problem when the thickness tends to zero.

中文翻译：

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法向阻尼响应接触中热弹性壳的数学和渐近分析

本文的目的是双重的。我们首先对热弹性中的动态接触问题进行数学分析，当接触由法向阻尼响应函数控制并且本构热弹性定律由 Duhamel-Neumann 关系给出时。在适当的数据假设下并使用 Faedo-Galerkin 策略，我们展示了该问题解决方案的存在性和唯一性。然后，我们研究可变形体实际上是壳的特殊情况，并使用渐近分析来研究当厚度趋于零时收敛到二维极限问题。