Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
IMPACT FACTOR 2016: 0.783
5-year IMPACT FACTOR: 0.792
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Source Normalized Impact per Paper (SNIP) 2016: 1.125
Mathematical Citation Quotient (MCQ) 2015: 0.43
Some inverse problems for acoustic equation in cylindrical domain
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.