Identification problems for Maxwell integro-differential equations related to media with cylindric symmetries

Abstract

As is well known, the propagation of electromagnetic waves in dispersive media is governed by integro-differential equations. We assume here that the medium is a rigid body with a cylindric symmetry. In this case all the physical characteristics, such as the dielectric coefficient, the magnetic permeability and the conductivity coefficient as well as the kernels accounting for memory effects, may be assumed to depend only on the distance from the axis of the cylinder. Our aim is to solve the inverse problem , consisting in determining, in addition to the electromagnetic field, also the relaxation kernels, by the means of additional measurements. Existence, uniqueness and continuous dependence results are proved in the context of suitable functional spaces.