ON THE FRECHET DERIVATIVE IN ELASTIC OBSTACLE SCATTERING

被引：24

作者：

Le Louer, Frederique ^{[1
]}

机构：

[1] Univ Gottingen, Inst Numer & Andgewandte Math, D-37083 Gottingen, Germany

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2012年 / 72卷 / 05期

关键词：

elastic scattering; Navier equation; Frechet derivative; far-field pattern; Dirichlet condition; Neumann condition; impedance condition; inverse scattering; BOUNDARY INTEGRAL-OPERATORS; FAR-FIELD; DIFFERENTIABILITY;

D O I：

10.1137/110834160

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the existence and characterizations of the Frechet derivative of solutions to time-harmonic elastic scattering problems with respect to the boundary of the obstacle. Our analysis is based on a technique-the factorization of the difference of the far-field pattern for two different scatterers-introduced by Kress and Paivarinta [SIAM J. Appl. Math., 59 (1999), pp. 1413-1426] to establish Frechet differentiability in acoustic scattering. For the Dirichlet boundary condition an alternative proof of a differentiability result due to Charalambopoulos is provided, and new results are proven for the Neumann and impedance exterior boundary value problems.

引用

页码：1493 / 1507

页数：15

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