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.
Publié le : 2019-04-04
Classification:
Lateral Cauchy data.,
Wave equation,
Unique continuation,
Quasi-reversibility,
Level set method,
Inverse obstacle problem,
2010 Mathematics. Primary: 35R25, 35R30, 35R35; Secondary: 65M60,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-01818956,
author = {Bourgeois, Laurent and Ponomarev, Dmitry and Dard\'e, J\'er\'emi},
title = {An inverse obstacle problem for the wave equation in a finite time domain},
journal = {HAL},
volume = {2019},
number = {0},
year = {2019},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01818956}
}
Bourgeois, Laurent; Ponomarev, Dmitry; Dardé, Jérémi. An inverse obstacle problem for the wave equation in a finite time domain. HAL, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/hal-01818956/