THE DOMAIN DERIVATIVE FOR SEMILINEAR ELLIPTIC INVERSE OBSTACLE PROBLEMS

被引：1

作者：

Hettlich, Frank ^{[1
]}

机构：

[1] Karlsruhe Inst Technol, Inst Appl & Numer Math, Karlsruhe, Germany

来源：

INVERSE PROBLEMS AND IMAGING | 2022年 / 16卷 / 04期

关键词：

Inverse obstacle problem; semilinear elliptic equation; domain deriva-; tive; Kerr type nonlinearity; iterative regularization method; GLOBAL UNIQUENESS; EQUATIONS;

D O I：

10.3934/ipi.2021071

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：691 / 702

页数：12

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