Identifiability and non-identifiability in acoustic tomography of moving fluid

Alexey Agaltsov (1) , Roman Novikov (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We consider a model time-harmonic wave equation of acoustic tomography of moving fluid in an open bounded domain in $\mathbb R^d$, $d \geq 2$, with variable sound speed $c$, density $\rho$, fluid velocity $v$ and absorption coefficient $\alpha$. We give global uniqueness results for related inverse boundary value problem for the cases of boundary measurements given for two and for three fixed frequencies. Besides, we also give a non-uniqueness result for this inverse problem for the case of boundary measurements given for all frequencies.

Mots clés: moving fluid; magnetic Schrodinger equation; acoustic tomography; inverse boundary value problems; identifiability and non-identifiability

Domaines: Equations aux dérivées partielles [math.AP]

Alexey Agaltsov, Roman Novikov. Identifiability and non-identifiability in acoustic tomography of moving fluid. Journal of Inverse and Ill-posed Problems, 2016, 24 (3), pp.333-340. ⟨10.1515/jiip-2015-0051⟩. ⟨hal-01150129⟩