The domain derivative for semilinear elliptic inverse obstacle problems

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI:10.3934/ipi.2021071

F. Hettlich

引用次数: 2

Abstract

We consider the recovering of the shape of a cavity from the Cauchy datum on an accessible boundary in case of semilinear boundary value problems. Existence and a characterization of the domain derivative of solutions of semilinear elliptic equations are proven. Furthermore, the result is applied to solve an inverse obstacle problem with an iterative regularization scheme. By some numerical examples its performance in case of a Kerr type nonlinearity is illustrated.

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半线性椭圆型逆障碍问题的域导数

在半线性边值问题中，我们考虑了在可达边界上从柯西基准面恢复空腔形状的问题。证明了半线性椭圆型方程解的定义域导数的存在性和一个性质。并将此结果应用于用迭代正则化方法求解逆障碍问题。通过数值算例说明了该方法在克尔型非线性情况下的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.