An inverse obstacle problem for the wave equation in a finite time domain. (English) Zbl 1410.35283
Summary: 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.
MSC:
| 35R25 | Ill-posed problems for PDEs |
| 35R30 | Inverse problems for PDEs |
| 35R35 | Free boundary problems for PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
inverse obstacle problem; quasi-reversibility; level set method; unique continuation; wave equation; lateral Cauchy dataReferences:
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