论文标题
与时间相关域中热方程的边界积分算子
Boundary integral operators for the heat equation in time-dependent domains
论文作者
论文摘要
本文为时间依赖性域的热方程的边界积分方程提供了一个功能分析框架。更具体地说，我们考虑了时空中的非圆柱形域，它是圆柱体的$ c^2 $ - 型形成图像，即时间间隔的张量和空间中固定域的张量产品。在非圆柱形结构域上，我们引入了Sobolev空间，跟踪Lemmata并通过模仿[M. Costabel，热方程，积分方程和操作员理论的边界积分运算符，13（4）：498-552，1990]。在这里，至关重要的是，Neumann Trace需要对移动边界的正常速度进行校正项。因此，必须仔细分析情况。
This article provides a functional analytical framework for boundary integral equations of the heat equation in time-dependent domains. More specifically, we consider a non-cylindrical domain in space-time that is the $C^2$-diffeomorphic image of a cylinder, i.e., the tensor product of a time interval and a fixed domain in space. On the non-cylindrical domain, we introduce Sobolev spaces, trace lemmata and provide the mapping properties of the layer operators by mimicking the proofs of [M. Costabel, Boundary integral operators for the heat equation, Integral Equations and Operator Theory, 13(4):498-552, 1990]. Here it is critical that the Neumann trace requires a correction term for the normal velocity of the moving boundary. Therefore, one has to analyze the situation carefully.
