A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem

被引：32

作者：

Baudouin, Lucie

Mercado, Alberto

Osses, Axel

机构：

[1] CNRS, LAAS, F-31077 Toulouse 04, France

[2] Univ Chile, Dept Ingn Matemat, Santiago, Chile

[3] Univ Versailles, Math Lab, F-78000 Versailles, France

[4] Univ Chile, Ctr Modelamiento Matemat, CNRS, UMI 2807, Santiago, Chile

来源：

INVERSE PROBLEMS | 2007年 / 23卷 / 01期

关键词：

D O I：

10.1088/0266-5611/23/1/014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a transmission wave equation in two embedded domains in R-2, where the speed is a(1) > 0 in the inner domain and a(2) > 0 in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that the inner domain is strongly convex and a(1) > a(2). As a consequence of this inequality, uniqueness and Lipschitz stability are obtained for the inverse problem of retrieving a stationary potential for the wave equation with Dirichlet data and discontinuous principal coefficient from a single time-dependent Neumann boundary measurement.

引用

页码：257 / 278

页数：22

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