Identification of conductivity and permittivity in a pulsed electric field model

We shall investigate the mathematical identification of the conductivity and permittivity in a pulsed electric field model for biological media. The conductivity and permittivity of the media are highly discontinuous, so their identifications are formulated into an output least-squares nonlinear minimization with BV-regularization. The regularizing effects and mathematical properties of the proposed regularizing system are analysed and verified. Then, the concerned nonlinear minimization problem is approximated by a fully discrete finite element method, and the convergence of the approximation is demonstrated.