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

Laurent Bourgeois 1, 2 Dmitry Ponomarev 1, 2 Jérémi Dardé 3 
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
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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Submitted on : Tuesday, June 19, 2018 - 5:19:39 PM
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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 , AIMS American Institute of Mathematical Sciences, 2019, 19 (2), pp.377-400. ⟨10.3934/ipi.2019019⟩. ⟨hal-01818956⟩



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