An inverse boundary value problem for the heat equation: the Neumann condition

被引:53
作者
Chapko, R [1 ]
Kress, R
Yoon, JR
机构
[1] Lviv Univ, Dept Appl Math & Comp Sci, UA-290000 Lviv, Ukraine
[2] Univ Gottingen, Inst Numer & Angew Math, D-37083 Gottingen, Germany
[3] Korea Adv Inst Sci & Technol, Dept Math, Taejon 305701, South Korea
关键词
D O I
10.1088/0266-5611/15/4/313
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider the inverse problem to determine the shape of an insulated inclusion within a heat conducting medium from overdetermined Cauchy data of solutions for the heat equation on the accessible exterior boundary of the medium. For the approximate solution of this ill-posed and nonlinear problem we propose a regularized Newton iteration scheme based on a boundary integral equation approach for the initial Neumann boundary value problem for the heat equation. For a foundation of the Newton method we establish the differentiability of the solution to the initial Neumann boundary value problem with respect to the interior boundary curve in the sense of a domain derivative and investigate the injectivity of the linearized mapping. Some numerical examples for the feasibility of the method are presented.
引用
收藏
页码:1033 / 1046
页数:14
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