论文标题
瞬态线性热弹性的边界积分配方，具有联合型边界条件
Boundary integral formulations for transient linear thermoelasticity with combined-type boundary conditions
论文作者
论文摘要
我们研究了由同质和各向同性域中的热弹性动力方程引起的内部/外部初始边界值问题的边界积分制剂。通过通往拉普拉斯域的通道，根据卢比奇的方法来处理时间依赖性。我们专注于其中一个未知字段满足DIRICHLET边界条件的情况，而另一个未知字段则符合Neumann类型的条件。在拉普拉斯域中，引入并证明了组合的单层和双层电位边界积分算子是强制性的。基于拉普拉斯域的估计，可以证明在时域中解决方案的存在和唯一性。该分析补充了以前的结果，这些结果可能会根据边界元素方法和卷积正交的联合使用而作为离散方案的数学基础。
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 single- 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.
