Inverse obstacle problems. (English) Zbl 1181.35334
Summary: We describe the main results on the uniqueness and stability of penetrable or impenetrable obstacles from various boundary data. We present basic ideas of proofs in the case of single and many boundary measurements. We discuss some methods of reconstruction. We consider the inverse problem of gravimetry, inverse conductivity and scattering problems, and similar inverse obstacle problems for hyperbolic and parabolic equations. We expose mostly known results and some new ideas and approaches. In conclusion, we list several open research problems of significance for theory and applications.
MSC:
35R30 | Inverse problems for PDEs |
78A46 | Inverse problems (including inverse scattering) in optics and electromagnetic theory |
31B20 | Boundary value and inverse problems for harmonic functions in higher dimensions |
35B35 | Stability in context of PDEs |