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Quantitative thermoacoustic tomography with microwaves sources. (English) Zbl 1386.35279

Summary: We investigate a quantitative thermoacoustic tomography process. We aim to recover the electric susceptibility and the conductivity of a medium when the sources are in the microwaves range. We focus on the case where the source signal has a slow time-varying envelope. We present the direct problem coupling equations for the electric field, the temperature variation and the pressure (to be measured via sensors). Then we give a variational formulation of the inverse problem which takes into account the entire electromagnetic, thermal and acoustic coupled system, and perform the formal computation of the optimality system.

MSC:

35M33 Initial-boundary value problems for mixed-type systems of PDEs
35Q61 Maxwell equations
49N45 Inverse problems in optimal control
80A23 Inverse problems in thermodynamics and heat transfer
93C20 Control/observation systems governed by partial differential equations
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