Abstract : We investigate a quantitative thermo-acoustic 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 enveloppe. 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.
