SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 3888-3911, January 2021.
We study boundary integral formulations for an interior/exterior initial boundary value problem arising from the thermo-elasto-dynamic equations in a homogeneous and isotropic domain. The time dependence is handled, based on Lubich's approach, through a passage to the Laplace domain. We focus on the cases where one of the unknown fields satisfies a Dirichlet boundary condition, while the other one is subject to conditions of Neumann type. In the Laplace domain, combined simple- and double-layer potential boundary integral operators are introduced and proven to be coercive. Based on the Laplace domain estimates, it is possible to prove the existence and uniqueness of solutions in the time domain. This analysis complements previous results that may serve as the mathematical foundation for discretization schemes based on the combined use of the boundary element method and convolution quadrature.

中文翻译：

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具有组合型边界条件的瞬态线性热弹性的边界积分公式

SIAM 数学分析杂志，第 53 卷，第 4 期，第 3888-3911 页，2021 年 1 月。
我们研究了由均匀和各向同性域中的热弹性动力学方程引起的内部/外部初始边界值问题的边界积分公式。基于 Lubich 的方法，通过通往拉普拉斯域的通道来处理时间相关性。我们关注其中一个未知场满足 Dirichlet 边界条件，而另一个满足 Neumann 类型条件的情况。在拉普拉斯域中，引入了组合的单层和双层势边界积分算子，并证明是强制性的。基于拉普拉斯域估计，可以证明解在时域中的存在性和唯一性。