Uniqueness of two phaseless non-overdetermined inverse acoustics problems in 3-d. (English) Zbl 1301.35214
Considering coefficient inverse problems in the frequency domain, it is usually asssumed that both modulus and phase of the complex-valued function representing the wave field are known on a certain set for global uniqueness results and reconstruction methods. However, it is impossible to measure the phase in many applications. Therefore, it is worthy to investigate coefficient inverse problems in the frequency domain, assuming that only the modulus of the scattered wave field is known on a certain set, that is in phaseless case. The current publication is aimed to prove uniqueness theorems for the phaseless non-overdetermined case of the 3-d acoustic equation in the frequency domain
\[
\Delta u + \frac{k^2}{c^2(x)} u =- g(x), \;\;x \in \mathbb R^3
\]
with the unknown spatially varying sound speed. The proof uses the basic properties of solutions to the acoustic equation, the tools of Fourier transform and analytic continuation of complex variable functions.
Reviewer: Elena V. Tabarintseva (Chelyabinsk)
MSC:
| 35R30 | Inverse problems for PDEs |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35L05 | Wave equation |
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