A Time Domain Formulation for Identi cation

We present a time domain approach for the investigation of dispersion mechanisms of a medium in electromagnetic eld problems. Maxwell's equations coupled with a generalized electric polarization model are considered. The polarization is given in terms of a convolution of the electric eld with an impulse response funtion. Existence, uniqueness and continuous dependence of solutions on data are presented for a one-dimensional dispersive medium case. Estimation of electromagnetic properties of media is demonstrated via numerical examples. Parameters representing the electromagnetic property of a medium may include the static permittivity, relaxation time, natural frequency, static conductivity, etc. depending on the polarization model chosen. Microwave images of tissue structures and soils play very important roles in many areas , including clinical and environmental medicine. These microwave images are useful in detection=enhanced treatment of abnormality of human organs and tissue, and detection= remediation of underground toxic wastes. The electromagnetic properties of a medium are generally characterized by its electric and magnetic polarization mechanisms and its static conductivity. Here we focus on the development of partial diierential equation (Maxwell's equations) based identiication techniques for physical and biological distributed parameter systems, with those for living tissue being a special case. We attempt to estimate the conductivity and parameters which characterize the polarization of media such as living tis