Boundary Integral Operators for the Heat Equation in Time-Dependent Domains

被引：1

作者：

Brugger, Rahel ^{[1
]}

Harbrecht, Helmut ^{[1
]}

Tausch, Johannes ^{[2
]}

机构：

[1] Univ Basel, Dept Math & Informat, Spiegelgasse 1, CH-4051 Basel, Switzerland

[2] Southern Methodist Univ, Dept Math, Dallas, TX 75275 USA

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2022年 / 94卷 / 02期

基金：

美国国家科学基金会;

关键词：

Heat equation; boundary integral equation; Time-dependent moving boundary; Non-cylindrical domain; NUMERICAL-SOLUTION; LAYER POTENTIALS;

D O I：

10.1007/s00020-022-02691-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. 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.

引用

页数：28

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