Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
IMPACT FACTOR increased in 2015: 0.987
Rank 59 out of 312 in category Mathematics and 93 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition
SCImago Journal Rank (SJR) 2015: 0.583
Source Normalized Impact per Paper (SNIP) 2015: 1.106
Impact per Publication (IPP) 2015: 0.712
Mathematical Citation Quotient (MCQ) 2015: 0.43
The system under consideration is governed by the equation utt = ∇ div u – rot µ rot u in Ω × (0, T); its response operator ("input output" map) RT plays the role of the inverse data. As in the case of the proper Lamé system, such a model describes a dynamical system with two wave modes (p-waves and s-waves) propagating with different velocities cp = and cs = correspondingly. We show that R2T determines and , where and are the subdomains of Ω filled (at the moment T) with p- and s-waves propagating from ∂Ω. Due to the wave splitting u = ∇p + rot s the problem is reduced to the inverse problems for the acoustical and Maxwell subsystems governed by the equations ptt = Δp and stt = −µ rot rot s with the response operators and determined by R2T . The first problem can be solved by the BC method (Belishev, 1986), the second one is solved by a version of the method based on a blow up effect. This version is the main subject of the paper. In addition, we derive the inequality, which can be used for approximate determination of the shape of .
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