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Journal Articles Inverse Problems and Imaging Year : 2019

An inverse obstacle problem for the wave equation in a finite time domain

Abstract

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.
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Dates and versions

hal-01818956 , version 1 (19-06-2018)

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Laurent Bourgeois, Dmitry Ponomarev, Jérémi Dardé. An inverse obstacle problem for the wave equation in a finite time domain. Inverse Problems and Imaging , 2019, 19 (2), pp.377-400. ⟨10.3934/ipi.2019019⟩. ⟨hal-01818956⟩
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