Stability in the determination of a time-dependent coefficient for wave equations from partial data

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:436

Article

Kian, Yavar^1,2 

[1] Aix Marseille Univ, CNRS, CPT UMR 7332, F-13288 Marseille, France

[2] Univ Toulon & Var, CNRS, CPT UMR 7332, F-83957 La Garde, France

关键词: Inverse problems;    Wave equation;    Scalar time-dependent potential;    Carleman estimates;    Stability inequality;   

DOI  :  10.1016/j.jmaa.2015.12.018

来源: Elsevier

【 摘 要 】

Let Omega be a C-2 bounded domain of R-n, n >= 2, and fix Q = (0,T) x Omega with T > 0. We consider the stability in the inverse problem of determining a time-dependent coefficient of order zero q, appearing in a Dirichlet initial-boundary value problem for a wave equation partial derivative(2)(t)u - Delta(x) u + q(t,x)u = 0 in Q, from partial observations on partial derivative Q. The observation is given by a boundary operator associated to the wave equation. Using suitable geometric optics solutions and Carleman estimates, we prove a stability estimate in the determination of q from the boundary operator. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free