Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
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Some inverse problems for acoustic equation in cylindrical domain
- Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Science, Acad. Koptyug prosp., 4, Novosibirsk, 630090, Russia. E-mail: email@example.com
We consider one- and multi-dimensional inverse problems for acoustic equation utt = c 2 (Δu – ∇ ln ρ· ∇u) in a medium filling interior of a cylinder infinite with respect to the variable z. For the one-dimensional problem of reconstruction of acoustic medium parameters (the velocity c(r) and the density ρ(r)) we present necessary and sufficient conditions of unique solvability. In multi-dimensional case we investigate the inverse problem of reconstruction of the velocity c(r, φ, z) assuming the density ρ(r) is known. Estimates of conditional stability are obtained in the both cases.