AN INVERSE OBSTACLE PROBLEM FOR THE WAVE EQUATION IN A FINITE TIME DOMAIN

被引：12

作者：

Bourgeois, Laurent ^{[1
]}

Ponomarev, Dmitry ^{[1
]}

Darde, Jeremi ^{[2
]}

机构：

[1] ENSTA ParisTech, Lab POEMS, 828 Blvd Marechaux, F-91120 Palaiseau, France

[2] Univ Paul Sabatier, Inst Math Toulouse, 118 Route Narbonne, GF-31062 Toulouse 9, France

来源：

INVERSE PROBLEMS AND IMAGING | 2019年 / 13卷 / 02期

关键词：

Inverse obstacle problem; quasi-reversibility; level set method; unique continuation; wave equation; lateral Cauchy data; QUASI-REVERSIBILITY; EXTERIOR APPROACH; SOLVE; SCATTERING;

D O I：

10.3934/ipi.2019019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an inverse obstacle problem for the acoustic transient wave equation. More precisely, we wish to reconstruct an obstacle characterized by a Dirichlet boundary condition from lateral Cauchy data given on a subpart of the boundary of the domain and over a finite interval of time. We first give a proof of uniqueness for that problem and then propose an "exterior approach" based on a mixed formulation of quasi-reversibility and a level set method in order to actually solve the problem. Some 2D numerical experiments are provided to show that our approach is effective.

引用

页码：377 / 400

页数：24

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