SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2463-2490, January 2020.
This paper is concerned with the application of time-domain boundary integral methods to a nonstationary boundary value problem for the thermo-elasto-dynamic equations, based on the Lubich approach via the Laplace transform. Fundamental solutions of the transformed thermo-elasto-dynamic equations are constructed explicitly by the Hörmander method. Simple- and double-layer potential boundary integral operators are introduced in the transformed domain, and their coercivity is established. Based on the estimates of various boundary integral operators in the transformed domain, existence and uniqueness results of solutions are established in the time domain. These results may serve as a mathematical foundation for the semidiscretization and full-discretization schemes based on the boundary element method and the convolution quadrature method for time domain boundary integral equations arising in thermoelasticity.

中文翻译：

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线性热弹性的时域边界积分法

SIAM数学分析期刊，第52卷，第3期，第2463-2490页，2020年1月。
本文基于通过Laplace变换的Lubich方法，将时域边界积分方法应用于热弹性动力学方程的非平稳边值问题。通过Hörmander方法明确构造了转换后的热弹动力学方程的基本解。在变换域中引入了单层和双层势边界积分算子，并建立了它们的矫顽力。基于变换域中各种边界积分算子的估计，建立了时域解的存在性和唯一性结果。